Conservative MP John Whittingdale has said Eurosceptic MPs could support Boris Johnson or Domic Raab to replace Theresa May.
Mr Whittingdale told talkRADIO’s Mike Graham there had been “non-stop” conversations about Mrs May’s resignation amongst Conservative MPs.
Mr Whittingdale said: “The Prime Minister is making it plain that she doesn’t wish to go but nevertheless the pressure for her to go from within the Conservative party is growing.
“There is certainly no shortage of candidates and any number of people who fancy their chances but I think serious candidates are much fewer.”
Although he refused to signal his support for any one candidate, he said the next Prime Minister must be a Brexit supporter.
He added: “I think it would have to be somebody who supported Brexit or ideally campaigned for Brexit in the referendum, who will go into those future negotiations determined to get the best outcome.
"According to the criteria I have set there are two in that category, Boris Johnson and Dominic Raab, both of whom resigned because they couldn’t support the Prime Minister’s agreement.”