The education secretary, Michael Gove, has attacked the "preposterous" number of Etonians in David Cameron's inner cabinet and, in the process, taken aim at the chances of Old Etonian Boris Johnson succeeding Cameron as party leader after the general election.

He described the concentration of Old Etonians as "ridiculous", adding that such a bastion of privilege does not exist in any other rich country.

Although Gove, in an interview with the Financial Times, stressed that the elite nature of Cameron's top team reflected the failings of past state education policies, the remarks fit perfectly with the Labour claim that the top of the Conservative party is an out-of-touch elite.

Gove drew comparisons between Cameron's team and the cabinet of the Eton-educated Tory prime minister Robert Gascoyne-Cecil, Lord Salisbury, who was criticised for alleged nepotism and cronyism.

"At the beginning of the 20th century, the Conservative cabinet was called Hotel Cecil," Gove said. "The phrase 'Bob's your uncle' came about and all the rest of it. It is preposterous."

Gove is the first Conservative education minister to send his child to a state secondary school, and has made it his stated mission to extend opportunities by trying to raise the standard of education through academies and free schools.

Cameron himself went to Eton, and the many Old Etonians in his inner circle include Oliver Letwin, minister for government policy; Jo Johnson, head of his policy unit; Ed Llewellyn, chief of staff; and Rupert Harrison, George Osborne's chief economic adviser.

"It doesn't make me feel personally uncomfortable because I like each of the individuals concerned, but it's ridiculous," Gove said. "I don't know where you can find some such similar situation in a developed economy."

Gove has recently been exposed briefing against Boris Johnson at a dinner with Rupert Murdoch. It is increasingly likely that Johnson, currently London mayor, will find a Conservative seat in time for the 2015 election, so he would be able to stand for the Conservative leadership if Cameron stands aside after defeat.

One of Johnson's chief rivals is likely to be Osborne, who went to St Paul's, another London private school.

Gove, himself educated at a fee-paying school in Scotland, said the composition of the party's high command was "a function of the fact that – as we pointed out a couple of years ago – more boys from Eton go to Oxford and Cambridge than boys eligible for free school meals".

Gove said in the interview that he did not want to be Tory leader, claiming that he lacked the "extra spark of charisma and star quality" possessed by others.