Mr Cameron wants to reach out to new voters

Edward Leigh told BBC Radio 4's Westminster Hour: "The core vote is not something that can be banked and then forgotten about."

Mr Leigh is a member of the Cornerstone Group of MPs, which backs tax cuts, immigration controls and use of the private sector in public services.

But he said Tory right-wingers would not return the party to civil war.

They were not criticising Mr Cameron but wanted to put forward their own policy ideas, he said.

'Intelligent voters'

Mr Leigh pointed to the Bromley and Chislehurst by-election as an example of the dangers of failing to get the Tory "core vote" to turn out.

The Conservatives held the seat but saw their majority from the 2005 general election slashed from 13,342 votes to 633.

Mr Leigh said Tory traditionalists were not like the "old Labour left".

"We are not a rump representing people who will always vote for us," he argued.

"These are intelligent voters and they want the party to articulate the case in a reasonable, outward looking way for tax relief, for fair and strong immigration controls, for private sector solutions."

Mr Leigh said it was possible for the Conservatives to remain true to their principles but present them in a more attractive way.

Recruiting women

Mr Cameron's efforts to recruit more women candidates in winnable seats have been boosted by the latest choices by Tory activists.

Labour had claimed the Tory A-list of elite candidates - more than half of whom are women - was failing to work as men were mostly being chosen to fight key constituencies.

This weekend banker Harriett Baldwin was chosen in West Worcestershire, where sitting Tory MP Sir Michael Spicer is stepping down.

And Karen Bradley, who has worked in Conservative headquarters, was selected in Staffordshire Moorlands, a new seat which the Tories believe they can win.

But men have still been chosen in eight of the 12 seats to have selected new candidates since the A-list was introduced.