David Cameron has been pitched into another row over his "Eton boys" government on the eve of a budget aimed at showing he is in touch with the concerns of ordinary voters.

Baroness Warsi escalated the issue by supporting earlier comments of education secretary Michael Gove that it was "ridiculous" there were so many Eton-educated men in Cameron's top team.

She was even pictured on TV with a mocked-up newspaper front page with a cartoon of Cameron and four of his chief aides under the headline: "Number 10 takes Eton mess off the menu".

The row is hugely embarrassing for the prime minister as it comes ahead of the budget which chancellor George Osborne is crafting in an attempt to show the government is helping the least well off and not favouring the rich and powerful elite.

Ministers are extremely sensitive to Labour ridiculing Osborne's "we're all in it together" slogan and attacks on the government as out of touch and always standing up for the wealthy.

So the interventions from Gove and Warsi are deeply unhelpful and play directly into the Labour assault.

It has been claimed that Gove was given a robust dressing-down by Cameron after his outburst, which some had seen by some as part of his alleged campaign to undermine would-be Tory leader Boris Johnson, an old Etonian.

But there is also a feeling in Westminster that the whole affair was an ill-judged attempt by the Tory high command to show they were themselves critical of the way individuals from certain social and educational backgrounds are over-represented at the top.

Osborne has played the row down, saying Gove was making a wider point about social mobility, something the government was attempting to tackle.

But Warsi's intervention has only made matters worse. Speaking on ITV's Agenda programme, she said: "Michael was making an incredibly serious point that it can't be right that the 7 per cent of kids who go to independent school end up at the top tables, not just of politics, but banking, and law, and every other profession.

"What Michael wants to create is a first class, world class state system which means that in future years you will have more pupils from state schools, people like me, around the cabinet table, and in that I fully support Michael Gove

Gove, who has pointedly announced his daughter is to go to a state secondary school, compared Cameron's team to the cabinet of Eton-educated Tory prime minister Robert Gascoyne-Cecil, the Marquess of Salisbury, who was criticised for alleged handing out jobs to relatives.

Old Etonians in the prime minister's circle include his chief of staff, Ed Llewellyn, the head of his policy unit and Boris' brother, Jo Johnson, senior policy minister, Oliver Letwin and Chancellor George Osborne's chief economic adviser, Rupert Harrison.

Osborne did not go to Eton, but the equally elite and expensive St Paul's.

The trouble with any ministerial attempt to highlight the problem of poor social mobility in this way is that it only serves to remind people just how top-heavy with those from privileged backgrounds the government is.