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Allies of Mr Sunak have contacted friends of the former Health Secretary, arguing that he does not have the support or 'infrastructure' and that they are competing for the same voters.
Mr Sunak stepped down after a major bust-up with Mr Johnson last weekend, with Mr Sunak allegedly having refused point black to cut corporation tax despite the PM's demands.
PICTURE EXCLUSIVE: The disgraced PM was seen hobnobbing with colleagues and officials, giving out hugs and cracking jokes as the group drowned their sorrows at Dover House
More than a dozen MPs are seriously mulling bids for the leadership after the PM's bombshell exit, with ministers raising fears the 'hounds of hell' have been unleashed.
The scale of the fallout emerged in Survation research carried out on Wednesday - before the PM finally accepted that his time in power was coming to a close.