David Cameron chose to make the grammar schools row a test of his leadership after private polling gave a warning that deserting voters believed that he was leading “the same old Conservative Party”.

The Tories’ biggest threat is not from UKIP or the BNP but the Liberal Democrats, according to secret research presented to the party’s front bench last month and leaked to The Times.

The polling also showed that voters are clearer about what they like and dislike about Mr Cameron than Gordon Brown and that Tory voters are much more positive about the Conservatives than the party’s activists.

Mr Cameron has faced the biggest revolt of his leadership over the past week after a speech by David Willetts, the Shadow Education Secretary, in which he said that the grammar schools were holding back children from poorer families. The Tory leader insisted that he did not set out to “pick a fight” over the issue of education and social mobility. But he had chosen to make it a “key test” after coming under heavy attack from MPs and the Tory grassroots.

Close allies said that he was determined to prove that the party was being consistent and to counter voters’ suspicions that it cared only for the well-off.

Evidence to explain his decision is contained in The State of the Conservative Party Brand. Stephen Gilbert, a former Tory campaign director, presented the document’s key findings to frontbenchers last month.

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