The two big beasts of the Tory right, David Davis and Liam Fox, issued a challenge to David Cameron on Tuesday morning when they jointly launched a new group within the party aimed at securing a majority at the next election by promoting "popular, radical conservatism".

While pledging loyalty, the Conservative Voice initiative is likely to be interpreted as a direct criticism of the prime minister, whose brand of liberal conservatism is blamed by many on the Tory right for the party's failure to secure an outright victory in 2010.

Speaking ahead of the launch on Tuesday morning, Davis said the aim was to "encourage seriously ambitious policy development and to help improve the party’s campaigning edge in really practical ways".

"Our approach is to work from inside the party and alongside the leadership - and to actively engage with think tanks, campaigning organisations, academics and business people," he said.

In an indication that Conservative Voice will seek to drag to Tory Party to the right, its founder Don Porter said he was keen to win back former members and voters attracted to the UK Independence Party and "to start dealing with that party head- on."

The group will seek to promote the free market economy, deregulation, low taxes a reduction in the size of the state as well as a looser relationship with the European Union.

The sight of Davis and former defence secretary Fox sharing a stage in Westminster is likely to fuel rumours of disquiet on the Tory benches at Cameron's leadership and that his reshuffle, which promoted many right-wingers, emboldened right-wing critics of the coalition rather than satisfied them.

On Sunday Tory backbencher Colonel Bob Stewart confirmed he had been approached by two party colleagues before the summer recess asking him to mount a "stalking horse" leadership challenge against the prime minister.

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Earlier this month Davis laid down the gauntlet to the prime minister and chancellor, calling for "radical" moves to rescue Britain's ailing economy.

The former shadow home secretary who challenged Cameron for the leadership in 2005 said recent GDP figures were "terrible" and warned the UK was at the "eleventh hour" in terms of avoiding decades of economic stagnation and unemployment.

Fox has been relatively quiet since being forced to resign as defence secretary in October 2011 following days of allegations that he gave his close friend Adam Werrity inappropriate access to the Ministry of Defence.

However the Thatcherite MP gave a high profile speech in July in which he argued Britain should negotiate a new relationship within the European Union, or hold a referendum on an exit. Today's appearance in Westminster is the latest step on his road to political recovery.

The new grouping also boasts leading backbench right-wing Tory MPs including Dominic Raab, Priti Patel, Robert Halfon and Steve Barclay.

Another member is Conor Burns, the MP for Bournemouth West who quit as a ministerial aide in July in order to vote against the government's plan to reform the House of Lords.

Since resigning Burns has been critical of the prime minister and has used his new found freedom to repeatedly mock the Lib Dems on Twitter.

"What is the point of Simon Hughes?" he asked last week while speculating that the Lib Dem annual conference would include lessons in "how to knit your own yogurt".

Speaking about the new group within the Tory party, Patel said it was designed to promote "Conservative ideas such as "aspiration, free enterprise and social mobility" whilst engaging voters of all backgrounds.

Another Tory MP attending the launch, Stewart Jackson, said he wanted to "get Cameron back on election winning ground" and away from the "current liberal mush".

The emergence of Davis and Fox as joint leaders of the new right-wing group comes as Downing Street has been forced to fight back against direct attacks from Boris Johnson.

The Tory mayor said the idea he was involved in a plot against the prime minister was "cuckoo", after it was reported Richmond MP Zac Goldsmith was prepared to stand down in order to allow Boris a speedy return to parliament.

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