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To some, they are just "an archaism" and "powerless figureheads" without purpose; to others, they are "passionate champions" and influential lobbyists for universities at a time when such support is desperately needed. Sir Robin Biggam, former chairman of the now-defunct Independent Television Commission, maintains that a person is qualified to be one only if he or she has reached "at least" the age of 50, while the former Liberal Democrat leader Sir Menzies Campbell proclaims that they should be "seen often and heard rarely".

The job of university chancellor, which is nearly 800 years old, is certainly peculiar. Partly it is about pomp and ceremony; as honorary head of the institution, chancellors are expected to dress - as the broadcaster and chancellor of the University of Roehampton John Simpson puts it - "in impossibly bright colours" in readiness to shake an astonishingly large number of hands on graduation day. Beyond that, the list of official duties is "laughably short", says Matthew Moss, private secretary to the vice-chancellor of the University of Cambridge - and for that reason, the post is "what the incumbent makes of it". But whatever one's view of their importance or otherwise, the fact that 5,558 academics and graduates turned out to vote in this autumn's election for the new Cambridge chancellor suggests that it is a role many care about.

From the former cricketer turned politician Imran Khan to actor Sheila Hancock, and the Archbishop of Canterbury to the musician Brian May, a quick scan of today's university chancellors (see related file, right) reveals that they are a diverse group who are doing an assortment of things in the wider world. Among UK universities, around 18 per cent of ceremonial heads could be described as "celebrities". Twenty-seven per cent come from the world of business, 26 per cent have a background in politics and 43 per cent are peers. Seven universities - including the University of London - are represented by royals. Ten honorary heads have a background in academia and 18 in the media.

All have busy lives outside academia and limited time to spare, so what can they contribute to their institution? Most obviously, a celebrity can raise the profile of a university and, perhaps, add an air of glamour; while those who are well connected in the worlds of politics or business might hope to win friends in high places and influence policy on their institution's behalf.

Other chancellors claim to care predominantly about their university's students. The former children's television presenter and Liberal Democrat peer Baroness Benjamin, who has been chancellor of the University of Exeter since 2006, aims to make "every single graduate and their family feel special". Benjamin experienced the joy of the occasion for the first time in 2005, when Exeter awarded her an honorary doctorate, an experience she describes as "the highlight of my life". As someone who left school at 16, on graduation day she felt as though she "had gone to the Moon and back". She now endeavours to attend every graduation ceremony, where she aims to make a connection, however brief, with each graduate. "I think to myself: 'Is this the one who'll create something scientific that will change the world? Will this one be prime minister? Will they be a teacher?' That's my excitement on greeting each graduate. That's the focal point. It's that moment between me and the student. I hope my words of encouragement to them will inspire them to go out and make a difference."

Not all chancellors are so confident of their ability to make an impact, however. On graduation day, Lord Adebowale, chief executive of the charity Turning Point and chancellor of the University of Lincoln, often imagines that "the people taking pictures will look back in four years and see this 6ft dreadlocked black guy and think 'who the hell is that?'"

The manner in which chancellors are appointed varies from institution to institution. At some universities, the senior management team, university councils or a mix of different university staff form a committee to choose their preferred candidate. Another method - used at institutions such as the universities of Oxford, Cambridge and Manchester - is for academics and/or graduates of the institution to elect the chancellor. The universities of St Andrews, Edinburgh, Glasgow, Aberdeen and Dundee have rectors as well as chancellors, who are elected by the students to represent them as chair of court.

Cambridge's system led, in October, to the most high-profile battle for a chancellorship in recent years. Lord Sainsbury of Turville, the former Labour science minister, was challenged by the actor Brian Blessed, a local shopkeeper Abdul Arain and the lawyer Michael Mansfield in the first actively fought contest for the Cambridge chancellorship since the Earl of Powis took on Prince Albert - and lost - in 1847.

More than 160 years later, Blessed vowed to "sweat blood" to increase opportunities for less privileged students. He also wanted to inspire expeditions and promised to promote "adventure, adventure, adventure". Arain, meanwhile, campaigned as part of a protest against a Sainsbury's store being opened near his corner shop and said he would connect town and gown in the city; and Mansfield said he would defend higher education from "market forces".

The election ignited plenty of debate about what a chancellor was for. In her blog, Mary Beard, professor of Classics at the University of Cambridge, said that Blessed was "the students' favourite, because they imagine that the chancellor of Cambridge is like a Scottish university rector, a sort of student mascot". Beard, who backed Sainsbury, was looking for something different: "Someone who might help in opening up the space for us to discuss widely the role of the university and educational priorities with government, funding bodies and the media - and who might help us get across our aims and policies better." The peer, who achieved 2,893 votes ahead of Blessed's 1,389, has promised to do just that: his mission statement declares that he will be "a passionate champion for Cambridge at home and abroad at a difficult time for universities". One blogger, however, saw victory for the establishment figure as "proof that academics suffer from group-think and like to play it safe".

It is not always easy to persuade a busy person to take on the role of chancellor. The psychologist and writer Tanya Byron turned down several offers of a chancellorship before she agreed to assume the post at Edge Hill University in 2008, because she was too busy "with two kids and a life". She says: "I never accepted because I thought it was something that would be great to do one day, but not now."

But she was won over by a visit to the institution. "The history of the university, the ideology, the philosophical stance on widening participation and social inclusion, which is very much what I do for a living: there was so much about it that felt really right for me." In particular, Byron admires the fact that Edge Hill was the first non-denominational teacher training college, and so the first place women could train to be teachers without the influence and control of the church. She now wears robes of heliotrope, green and gold, colours thought to relate to the suffragette movement.

The idea of finding a university that is the right personal fit resonates with many of the chancellors who spoke to Times Higher Education about their role. Benjamin thinks that for every chancellor, there is "a right university for you and your character".

Despite being keen to take on the position of president of the Central School of Speech and Drama - the school's version of a chancellor - the theatre director Michael Grandage says that he thought long and hard about the offer. In the end he decided to accept it because of his personal connection to the school, where he had studied to be an actor. He sees his role as linking the school's past to its present and future. "The graduates past are as much a part of the DNA of the place as the future. When I was asked [to be president], it wasn't something that was out of the blue and made no sense."

Naturally, many chancellors are graduates of the institution they represent. The former BBC director general Greg Dyke, who has been chancellor of the University of York since 2004, is also an alumnus of the institution he heads. For him, part of the appeal, aside from his "enormous affinity and fondness" for York, is how unlikely his future appointment would have seemed when he was a mature student. "The academics would have been surprised, and the administration would have been astonished."

Many chancellors say that the benefits for the chancellor and for the university flow both ways, and extend far beyond the honour of being appointed; some chancellors claim that the position can have a great impact on them personally. Byron says her role helps her to familiarise her children with higher education. However, she admits that her friends and family don't always show respect for the office. "My kids think it's hilarious. When I had my hat put on me at my first graduation ceremony, you could hear the entire front row, my friends and family, just wetting their pants with laughter. There's a picture of me in my gear in the downstairs toilet."

Grandage, meanwhile, says that he is grateful for the opportunity his role has given him to learn more about the sector. "It has put me much more directly in touch with the political landscape of higher education in a way I couldn't do by reading a newspaper."

And Dyke enjoys being the public face of a network of graduates. "What is really interesting is the number of people who come up to me and say, 'You went to York, so did I.' I sat in the theatre the other day and a guy turned around and said to me 'You gave me my degree last year' - that happens all the time."

Sometimes, inevitably, things go wrong. Some appointments, for instance, go down better than others. Grandage says that Central's choice of the Labour politician Lord Mandelson as its chancellor in 2001 caused some consternation, but he adds that it also led alumni to reflect seriously on the role of chancellor. "That was the first time a lot of us thought about what that role means and what the significance of it is."

Meanwhile, in 2009, the Olympic athlete Brendan Foster stepped down from his role as chancellor of Leeds Metropolitan University following the resignation of Simon Lee, then vice-chancellor. It later transpired that Foster had tried, unsuccessfully, to step in and mediate between Lee and the chair of governors, Ninian Watt, after relations between the two broke down.

Dyke's advice to chancellors is to avoid getting too involved in the politics of the organisation. Chancellorship, he says, is "all the fun without any of the responsibility".

But, despite their lack of formal power over their institution, chancellors maintain that they can still play a key role in the smooth running of a university. Adebowale strives to support Lincoln's vice-chancellor, describing the position as "a beautiful role in a way; being able to observe without having the responsibility...is quite nice. I'm not Mary Stuart's boss; I'm just someone who is there to support in a leadership capacity if and when she wants it and sometimes to drop the odd fizzing tablet in the water." And Paul Thompson, rector of the Royal College of Art, says that the need for accountability is what makes his institution's equivalent to a chancellor - Sir James Dyson, the college's provost - so invaluable. "Ultimately you have to have someone who is the titular head of an organisation, someone who I can report to as chief executive; otherwise there would be no check and balance. I don't think we would have any credibility if we didn't." The former Conservative prime minister Harold Macmillan once joked that chancellors existed because without one there could be no vice-chancellor; perhaps his jest contained more than a grain of truth.

But some academics remain steadfast in their scepticism. There are doubts about the value of the criteria used to select candidates and about the true motives of the incumbent. Sharon Wheeler, lecturer in journalism at the University of Portsmouth, fears that the desire for publicity can mean that a more flashy candidate usurps someone who is less well known but has a stronger connection to the university. "A lot of the time it feels like it's more a matter of how outlandish a person can be nominated and/or appointed, rather than whether they're genuinely going to be interested in the university and actually get involved in events outside of glad-handing at degree ceremonies."

Peter Lennox, group director of the Signal Processing Applications Research Group at the University of Derby, believes that chancellors are there "to lend an ear to insincere sycophantic drivel spouted by the ambitious", while a senior lecturer at the University of Chester who asks not to be identified says that "a university chancellor is an archaism; a powerless figurehead who fancies herself or himself as an oligarch overseeing a public sector institution".

Perhaps Lord Patten of Barnes, who describes himself as "the nearest thing there has been to a serial chancellor" (he is chancellor of the University of Oxford and, until 2009, combined this with chancellorship of Newcastle University; when he was governor of Hong Kong, he was chancellor of all the Hong Kong universities), is best qualified to respond to such criticism. He once explained the purpose of chancellors thus: "All of us, as chancellors, have to promote the importance of higher education in our society. Universities need all the friends they can get."