David Cameron has been warned by a former head of his local county council that he and George Osborne have been portrayed as "public school toffs" and need to do more to develop the "natural appeal" of Ukip's leader, Nigel Farage.

In a powerful critique of the Tory leadership, Keith Mitchell – for more than 10 years until 2012 the Conservative leader of Oxfordshire county council – said the prime minister and chancellor needed to "speak the language of Joe public".

Mitchell wrote his comments on a blog after the Conservatives lost control of the council.

A strong performance by Ukip at the elections this year on 2 May squeezed the Tory vote, and Oxfordshire, which covers the prime minister's Witney constituency, became a hung council.

He wrote: "I am afraid the Ukip leader has a style and a manner of speaking that connects with ordinary mortals much better than professional politicians. He is unafraid to be filmed with a pint of beer and a cigarette in his hand when all of our media training tells us to eschew either image.

"He also uses soundbites that appeal to Conservatives. I suspect many are unrehearsed – again something professionals are trained never to do.

"You, and George, in particular, have been portrayed as public school toffs. You have to work out how to be one of us without affectation or silly gimmicks and to speak the language of Joe public."

Mitchell said that government plans to legalise gay marriage, and the issue of Europe, did not feature much on the doorstep. But he said he detected a "perception of disconnection, of ministers being part of a metropolitan elite, far removed from day-to-day pressures".

The former council leader added: "Margaret Hilda [Thatcher] used housewife terms to talk about complex financial and economic issues. Above all, it is how people feel that is determining public opinion: call it the economy; call it public wellbeing; call it job opportunities. Electors protested [on 2 May] about a perception of being 'out of touch'."

Mitchell said that Cameron could turn his fortunes round, though he would have to combine attributes of both Winston Churchill and Thatcher.

"I understand how hard this is and the conflicting pressures on you, but people want a clearer and stronger style of leadership that speaks the language of conviction and leadership. Churchill gave it in the war against Hitler. Thatcher gave it when our country was again under threat.

"Today, we face a crisis of belief in our institutions and our politics. You have the capacity to rise to this challenge but it will take the charisma of Churchill and the conviction of Thatcher to deliver."