Former Conservative leadership candidate David Davis has attacked the top of the party as "privileged and out of touch" in the wake of the losses to Ukip in the local elections.
Davis said David Cameron needed to show he understood the concerns of ordinary people.
In an article for the Daily Telegraph, Davis said he had "no answer" to constituents who asked why Old Etonians were seemingly given preferential treatment.
He gave the example of Nadine Dorries, "a girl from a Merseyside council estate," who was suspended from the Tory party, while Old Etonian Jesse Norman, who had rebelled against the government as a backbencher, was promoted to the Downing Street team.
With the Tories losing 340 councillors and the control of 10 councils, some Tory right-wingers called on the Prime Minister to firm up his commitment to holding a referendum on Britain's membership of the European Union to counter the appeal of Ukip.
However Davis said the priority for Cameron - who recently appointed Old Etonian Jo Johnson to head the No 10 policy unit - was to reconnect with voters who thought the Conservatives lived in a different world to them.
"The fact is that if we want to win the next election, we have to break this impression of being privileged and out of touch," he wrote.
"The British public are neither snobs nor inverted snobs, but they do expect the Government to understand their problems and do something about it.
"That means more straight talking and fewer focus groups; more conventional Tory policies, not because they are Tory, but because they work; less pandering to metropolitan interest groups; and please, please, no more Old Etonian advisers."
Home Secretary Theresa May was reluctant to discuss his attack on Saturday morning, as she talked up the Tories' pledge for an EU referendum.
However she rejected calls - including from Davis - to bring forward the date of the referendum and stage it in this parliament in order to finally kill off the appeal of Ukip to Tory voters.
She said that it was important that they stood by David Cameron's plan to re-negotiate the terms of Britain's membership and then put the new settlement to the country.
"If you want to take a re-negotiated settlement to the British people, you have got to re-negotiate it," she told the BBC Radio 4 Today.
"We can look at whether we can give some greater certainty in terms of the referendum. I think what we need to do is to
be able to show people that we will hold that referendum, we will hold that referendum after the general election."