The Conservatives must “break the impression of being privileged and out of touch” if they are to stand a chance of winning the next general election, former leadership contender David Davis has warned.

Speaking after the party suffered heavy losses to the UK Independence Party in the local council elections, the MP for Haltemprice and Howden said David Cameron should stop surrounding himself with fellow Old Etonians and show he undersood the concerns of ordinary people.

With the Tories losing 340 councillors and the control of 10 councils, some Tory right-wingers have 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, Mr Davis said the priority for Mr 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 said in an article for The Daily Telegraph.

“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 advisors.”

Home Secretary Theresa May, who has been touted as a possible future Tory leader, refused to be drawn on the argument, and insisted the party was focused on “bringing people back to voting Conservative”.

She told Sky News: “The Government has shown that it understands some of the problems that hard-working people are facing – the efforts we’ve taken to helping local councils freeze their council tax, hold down fuel duties, two million people have been taken out of paying income tax, and an income tax cut for 24 million people.

“There are other areas we know the task is a sizeable one – controlling welfare and immigration. We are already on the right track in dealing with these issues.”

She added: “What we will be doing over the next couple of years is working hard to bring people back to voting Conservative – showing them what we are doing in those areas … and how the choice in the next election will be Conservatives who will control welfare and immigration and deal with the deficit, and the same old Labour Party who will just ask for more spending, more borrowing, more debt.”

UKIP’s gains of 131 councillors in the council elections were dubbed a “game changer” by leader Nigel Farage.

While Labour made gains – picking up 268 councillors and taking control of two councils – analysts said they fell short of the numbers needed to show that Ed Miliband was on course for Downing Street.

For the Liberal Democrats it was another grim set of results with the loss of 110 councillors while crashing to a humiliating seventh place in the South Shields parliamentary by-election, just ahead of the Monster Raving Loony Party.

Mr Cameron pledged to work really hard to win back voters who abandoned the Conservatives for the UKIP, promising action to turn round the economy, cut immigration and sort out the welfare system.

Having previously derided UKIP as “fruitcakes, loonies and closet racists”, the Prime Minister adopted a softer approach, promising to show “respect” for those who voted for them.

Mr Miliband insisted that Labour had made “good gains” but acknowledged there was “more work to do”.

“These elections show many people have lost trust in David Cameron’s ability to change Britain. But our task is to win the trust of the people we haven’t yet persuaded that Labour can make the difference,” he said.

Deputy Prime Minister Nick Clegg said the Lib Dems’ poor showing reflected their journey from “a party of protest to a party of government”.

“I have always said it is understandable why it is that people might be attracted to the simple answers that the UK Independence Party is offering to deal with this country’s complex problems,” he said.

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