How could you have secured two weeks’ work experience this summer at a top London law firm or with John Redwood, the Tory MP? Simple: by paying for it. Or perhaps you would have preferred two weeks at Theo Fennell, the celebrity jeweller, or with the Ambassador Theatre Group or an international property firm?

All those opportunities and more were for sale recently in an auction run by Millfield, the independent school known more for sporting prowess than academic excellence. There’s just one snag: the only people who could bid for such prized work experience were parents of pupils, or alumni of the school, where fees are £6,285 a term .

Still, at about £500 a pop, the work experience was cheaper than that auctioned in February at the Conservative Black & White ball, where two weeks with city firms sold for £3,000. And it was vastly cheaper than the unimaginable £4,000 that someone paid for one week at the men’s style magazine GQ at a charity auction last year.

Such events may suggest that getting daddy to buy an elite work placement is the expensive face of a “new-style old-boy” network. Certainly Nick Clegg, the deputy Prime Minister, believes that in modern Britain, privilege begets privilege.

Recently, Clegg launched the coalition government’s strategy for social mobility, called Opening Doors, Breaking Barriers. In it, he declared, “Patterns of inequality are imprinted from one generation to the next.” Drawing attention to the moment when young people embark on the world of work, he called for “fairer, more open internship and work experience programmes.”

In an article, Clegg went further: “In politics, as in the media, and in many other popular professions, who you know is increasingly becoming more important than what you know.”

Quite apart from accusations of hypocrisy — Clegg benefited as a young intern from family connections and his stance raised tricky questions. Does “who you know” really count in today’s competitive business environment? Are internships unfair? If so, what can be done to make them fairer? And let’s clear up one point: work experience and internships are not the same.

Both are likely to be unpaid but work experience is what schools encourage students to do for a couple of weeks after their exams. Internships may occur before, during or after university, and last for two or three months.

Britain’s recent record on social mobility is poor. Government figures show only 25 per cent boys from working class backgrounds end up in professional or managerial jobs. Almost half of those born to parents in the top quartile of earners end up being top earners themselves, while only 11 per cent of those from low-income homes move up to that level.

In the UK and the US, social mobility is lower than in Canada and Scandinavia. However, the causes are less clear, especially in relation to internships. Students, current and recent, said that effort and educational attainment were more important in landing internships than “who you know”, and that family links are of limited help.

One admitted that his father, who works for one of the most gilded investment banks in London, had helped him get an interview for a three-month unpaid internship at the bank. He still didn’t land the post.

Another said, “I had a friend whose dad is chairman of a major private equity firm. He gave three of us six-month internships.”

Did it line up a future job? The former intern, now a graduate of Bristol University, said, “I was quite young and went out and got pissed most nights. I was asked to leave after a month. The boss walked past when I had my feet on the desk.”

Elaine, 19, rejected the opportunity her father lined up for her last year at a London investment firm, preferring politics. “I heard about David Miliband’s campaign for Labour leader,” she said. “It sounds ridiculous but I just walked in .”

From the Internet she found a contact number, called up and volunteered her help. “They said, I could come in. I had done A-level politics, which was the extent of my involvement. Then on my first day, two hours into manning the phones, David Miliband walked in and I met him.”

She went on to do more unpaid work at a think tank and a political blog. She recounted how a female Labour aide interviewed her at Westminster. “She told me straight off there wouldn’t be any pay or expenses. She suggested I use my own laptop and work in the local Starbucks.”

She accepts that being unpaid is not the best of circumstances. “I’d love to be paid, but the experience is far more valuable.”

Alan, who spent two months as an intern with a London MP after winning the post out of the blue, is less sanguine. He said he was only able to afford to be an intern by using funds intended to cover his university costs. He was allowed £3 a day for food and other expenses, but was unable to claim for a doughnut because it was “frivolous”. Another young hopeful, David, had three internships at Westminster before landing a paid job. He says, “Unpaid internships are not just exploitative of individuals, they also restrict social mobility. Talent is distributed throughout the population, but we are only picking from a tiny tier, based on parents’ bank balances.”

MPs seem reluctant to embrace change, even at Westminster. Recently, Clegg said that in future the Liberal Democrats would pay “proper remuneration” to interns. But an aide to John Leech, a Liberal Democrat MP, promptly let slip that Clegg’s promise would not apply to MPs, but only to Liberal Democrat headquarters.

During his campaign for the Labour leadership Ed Miliband promised to support pay for interns. Yet Labour has used at least 20 unpaid interns since Miliband became leader, according to Intern Aware, a website.

The problem is that if organisations are forced to pay interns, they may stop offering them any opportunities at all. Nicholas Lakeland, a partner at Silverman Sherliker, a London law firm, which takes interns, agrees. “Interns are not that useful, to be truthful,” he said. “It’s really much more for them than it is for us. If we had to formally put them on the books, nobody would bother.”

That said, Lakeland believes the increasing use of interns for long-term work is giving rise to abuses. Unlike “apprentice”, “worker” or “employee”, there is no legal definition of an “intern”. It is a grey area where or when work experience or internship turns into unpaid or cheap labour.

“Our advice generally is that you should limit an internship to eight weeks,” said Lakeland. “Beyond that, it starts to look like doing loads of work for free. There are some industries where they do exploit interns.”

Some see the internship debate just a symptom of more fundamental problems in education and the economy. Improving education standards is vital, as Clegg’s report observes. But so is helping bright children from poor backgrounds to have make connections and have the confidence to use them. Schemes such as Pathways to the Professions, run by Edinburgh University with help from the Sutton Trust, aim to give guidance to state school students.

Beyond that, the even bigger issue is the general availability of work opportunities, according to Diana Furchtgott-Roth, an Oxford-educated former chief economist at the US Department of Labor. She said: “A major barrier to social mobility is lack of employment opportunities and job growth. When jobs are plentiful it is easy not just to get a job, but also to move up.”

Her solution: reduce labour market regulations and not increase them. “Internships,” she says “give the employer the opportunity of trying out a worker at low cost. Do well, and the employer may keep you. Put your feet up — and even if Daddy has bought your two weeks of work experience, you may not last.”