London (CNN) The race to succeed Theresa May as British Prime Minister is entering its crucial stage. In the next two days, Conservative lawmakers will select two candidates to be paraded in front of the wider party membership for a final decision on who will take on the fateful (and twice fatal) Brexit chalice.

But something strange has happened. All the attention is not on the rockstar front runner, Boris Johnson , but an insurgent outsider.

Rory Stewart, the current international development secretary, has been the hands down star of this leadership race. Initially scoffed at by Conservative commentators, Stewart, a self-declared centrist who still backs Theresa May's Brexit deal, has seen off five candidates, all of whom stood on much harder Brexit platforms. His campaign has clearly spooked the others, who are seeing some of their supporters defect to Stewart.

Improbably, on Tuesday he made it through to the next round of voting, winning the support of 37 Conservative members of Parliament -- up from 19 in the last round. It was the biggest leap forward of Johnson's remaining rivals.

On the face of it, Stewart's campaign looked doomed to fail. He was virtually unknown before the contest began, with barely a month's experience in May's Cabinet and a low-profile job as a junior prisons minister before that. Pitching himself as the only candidate telling the truth about Brexit, Stewart says that May's deal with Brussels is the only one any prime minister can realistically secure. He says that candidates claiming they can take the UK out of the EU without a deal are lying — because Parliament will not realistically allow them to do it.

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