The failure of employers in elite professions such as law and the media to stop using unpaid interns in the face of warnings must be met with a ban on the “unfair” practice, the government’s social mobility commission will recommend this week.

The most sought-after professions have become even less representative than the most selective universities, with jobs in effect closed off to those without a network of contacts and significant financial support. Only 4% of doctors, 6% of barristers, 11% of journalists and 12% of solicitors have working-class origins, according to recent research by the London School of Economics using Labour Force Survey data. In its end-of-year report to parliament, the commission warns that Britain remains “a deeply elitist nation where the chance of getting a well-paid job in a top profession is still strongly correlated with social background”.

It adds: “It is time to treat internships as part of the formal, not informal, labour market. In our 2014 state of the nation report we said that unless we found evidence that the employers were taking action to end the unfair activity of unpaid internships, the government should bring forward legislation to ban them.

“Unfortunately, we have been able to find little such evidence. As a result, the commission believes it is high time that internships are defined in law and unpaid internships banned.

“Any work placements that last more than four weeks should be classified as internships and those doing them should receive at least the minimum wage.”

Internships ranging from a few weeks to a year or more have become a prerequisite for access to the professions, the commission will claim.

The vast majority of internships are said to be in London, where the cost of living is highest. With the average cost of renting a room in London £743 a month and a monthly travel card more than £100, an internship can cost more than £1,000 a month to fund.

“The damaging impact of unpaid internships on social mobility cannot be overstated,” the commission’s report will say. “Young people without financial support from their parents are effectively excluded due to means not merit and potentially locked out from sought-after careers entirely.”

The commission, chaired by the former Labour cabinet minister Alan Milburn, finds that people from working-class backgrounds – even high attainers – are less likely to secure such jobs because they have “less access to networks and knowledge to navigate the system than their more affluent peers”.

The proportion of those in elite occupations coming from non-professional or managerial backgrounds was only four percentage points greater (50%) in 2014 than it was in 2005.

Just over three years after graduating in 2010-11, those from the most disadvantaged backgrounds were 11% less likely to be in professional employment than those from the most advantaged.

Facebook Twitter Pinterest Only 6% of barristers have working class origins. Photograph: Bloomberg/Bloomberg via Getty Images

People whose parents worked in higher managerial and professional occupations make up only 14.7% of the population, but 27.2% of them end up in those occupations. Conversely, those with parents who worked in routine or semi-routine employment form 31.7% of the population, but only 17% of those who end up in top jobs.

The commission, whose deputy chair is former Tory cabinet minister Baroness (Gillian) Shephard, welcomes new recruitment processes brought in by some employers, such as looking beyond high academic results, lowering or removing Ucas points for graduate entry and introducing “CV blind” interviews.

But it finds that the medical profession has “found it much harder to open up … to those from disadvantaged backgrounds. Others, like the Bar, risk becoming even more socially exclusive”. The report adds: “In the arts and media, the dramatic rise in unpaid internships and practice of securing work experience through contacts is closing off these careers to all but those from privileged backgrounds.”

If you’re at a state school, you’re less likely to reach the top professions than if you are educated privately Theresa May

Nearly half of the recruiters who took part in the High Fliers 2016 graduate labour market survey stated that graduates with no previous work experience would have little or no chance of receiving a job offer from their organisation.

According to the same research, 32% of new entrants are recruited by top graduate recruiters from internship programmes; in banking, it is as high as nearly 80% of the graduate intake.

Theresa May has claimed that tackling social inequalities is a priority and has criticised the current situation where: “If you’re at a state school, you’re less likely to reach the top professions than if you are educated privately.”

The new prime minister’s cabinet has the lowest proportion of ministers who went to private school in more than 70 years, with 70% state-educated.

However, the report says that evidence from some firms lays bare that real progress will only be made if leading employers radically reform recruitment practices.

The commission in partnership with the Social Mobility Foundation has launched a Social Mobility Employer Index which will benchmark firms’ efforts in areas such as recruitment, selection and progression.

The report says that the index will be run with the aim of “encouraging employers to compete to recruit, and to keep, the best and brightest candidates from lower socioeconomic backgrounds”, but denies that it is seeking to name and shame the worst performers. The final rankings will be announced in the spring.