David Cameron, the British opposition leader, can contain demands for tax cuts from Conservative rightwingers without “blood on the carpet”, his policy chief has predicted, as a poll suggests the party has finally emerged from the shadow of Margaret Thatcher.

In an interview ahead of the party’s annual conference, starting in Bournemouth on Sunday, Oliver Letwin said he was “not deluded” about the scale of the electoral challenge facing the party. The Tories need to more than double their 3 to 4 percentage point opinion poll lead to win an outright majority.