Young people from working-class backgrounds are being systematically excluded from jobs in top legal and accountancy firms, an official report has found.

The chairman of the Social Mobility and Child Poverty Commission, Alan Milburn, accused firms of imposing a "poshness test" effectively excluding recruits whose parents do not have "the right sort of bank balances".

A study of 13 "elite" law, accountancy and financial services firms carried out for the commission found that 70% of job offers last year went to graduates who had been to fee-paying or selective state schools.

London Mayor Boris Johnson and the City of London Corporation (CLC) both called for greater social mobility, with Mr Johnson, himself an Old Etonian and Oxford graduate, saying firms should focus on the "skills, talent and energy" of applicants, rather than what school they went to.

Former Labour cabinet minister Mr Milburn said the findings should be a "wake up and smell the coffee moment" for employers who needed to ensure their recruitment practices were "genuinely meritocratic".

"This research shows that young people with working-class backgrounds are being systematically locked out of top jobs," he said.

"Elite firms seem to require applicants to pass a 'poshness test' to gain entry. Inevitably that ends up excluding youngsters who have the right sort of grades and abilities but whose parents do not have the right sort of bank balances.

"In some top law firms, trainees are more than five times likely to have attended a fee-paying school than the population as a whole.

"They are denying themselves talent, stymying young people's social mobility and fuelling the social divide that bedevils Britain."

The survey found that, at leading accountancy firms, typically 40% to 50% of applicants had been educated at the elite Russell Group universities and that they received 60% to 70% of all job offers.

It said that this was "a direct result of elite firms' recruitment and attraction strategies".

It urged firms to overhaul their recruitment policies to encourage candidates from a wider range of educational and socio-economic backgrounds, while ensuring they had similar levels of support to those enjoyed by their more privileged peers.

New Uxbridge and South Ruislip MP Mr Johnson agreed there was an imbalance in the type of graduates that tops firms were recruiting. Speaking at an event in Camden to mark the launch of London Technology Week, he said: "I completely agree. I think the answer is to look at what is happening, for instance in London schools where there have been massive improvements in the last 10 or 20 years to make sure that everyone is given a fair crack of whip."

He continued: "London is the most successful city on earth at the moment, because everybody has a chance. We are trying to make sure that we widen the opportunities as much as we can."

Mark Boleat, the CLC policy chairman, said: "Today's report indicates a huge threat to Britain's social mobility and our economic growth. While more employers are creating paid internships and apprenticeships to attract bright young people from disadvantaged backgrounds, too many are still guilty of hiring in their own image.

"Drawing from a narrow pool of private school and Russell Group educated applicants will lead to a skills shortage and generation of wasted talented."

The Law Society said 450 companies had signed up to its Diversity and Inclusion Charter, almost twice the number in 2013.

A spokeswoman added: "By working closely with law firms, we aim to support the profession to share best practice and to demonstrate that good diversity, inclusion and social mobility policies give a competitive advantage."

The Institute of Chartered Accountants in England and Wales said the industry was working to attract talent regardless of background but the report showed still more needed to be done.

Director Sharon Spice said: "We are starting to see a trend among employers in recruiting chartered accountants, which will go some way to address social mobility.

"The numbers of trainee accountants are at an all-time high, but the way they enter the profession is looking different. Last year, the proportion of those with a degree dropped for the first time with employers having a growing appetite to recruit school-leavers and apprentices. Trainee accountants with degrees reduced by 3% between 2013 and 2014 alone.

"Widening access to accountancy is a shared challenge between employers, schools, young people and professional bodies, so we must work together."