Ms Mordaunt is the new 6/1 favourite on Betfair Exchange to replace the current prime minister, with Jeremy Hunt’s odds drifting to 13/2 from 4/1 in the past week.
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Foreign secretary Liz Truss is in third place to replace the prime minister, with odds of 15/2.
The new odds also show that Mr Johnson is 5/2 to leave his role this year and 11/2 to depart in 2023, with the party 3/1 to gain an overall majority at the next General Election.
The news comes nearly a week after Conservative MPs called for a vote of no confidence against the prime minister following anger over the Downing Street parties and the recent Sue Gray report.
Ahead of the vote, Ms Mordaunt told The News that: ‘I didn’t support him in the leadership contest but he has always had my loyalty because I think that’s what you do when you have a democratic process – you select a leader and then you owe that person your loyalty.’
The results of the vote of no confidence concluded that Mr Johnson had won by 211 to 148, meaning that he can continue as the leader of the Conservatives.Ms Mordaunt has been approached for comment.