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By Beth Rigby, deputy political editor

The Sunday political chat shows were a sight to behold last weekend as would-be successors to Theresa May took to the small screen to parade their wares.

Matthew Hancock, the health secretary, and Brexiteer Dominic Raab pitched up on Sky's Sophy Ridge on Sunday, while foreign secretary Jeremy Hunt and former Brexit secretary David Davis settled into the Andrew Marr sofa.

The beauty parade of PMs-in-waiting that has for months been rumbling along in the back rooms of Westminster is now in shifting to the stage

From backbenchers to cabinet ministers, the Conservative party has collectively decided the time is coming for Mrs May to stand down.

In one recent conversation a cabinet minister was openly talking to me about when she would step down, suggesting that a summer leadership contest with Mrs May's successor anointed at party conference in October was a most likely outcome.

The following day another figure in Mrs May's cabinet told me they expected the prime minister to announce she was standing down at party conference, and that her husband, Philip, should stage an intervention before the party drags her out of No 10 in another confidence vote in December.

"It's better that she goes on her own terms than waiting for the Brexiteers to take her out," said the cabinet minister.

And all of that chatter came before she lost a vote on her Brexit deal for the second time on Tuesday night by a substantial 149 votes, and with it any semblance of control of her party or the Brexit process.

Failed politics and a failing prime minister, Sir Bernard Jenkin voiced what many of her colleagues have been muttering under their breath on Tuesday night as he told me on Sky News that this was a "very time-limited administration".

In December Mrs May survived the biggest parliamentary defeat ever suffered by a sitting prime minister on her Brexit deal: a vote of confidence in her leadership (giving her a year's grace until the next ballot) and a vote of confidence in her government.

Now forced to hand over control of Brexit to parliament, it is but a matter of time before she has to stand down. But who replaces her is a wide and open field, with a dozen or more Tories thinking of running.

So in a nod to this week's Cheltenham Festival, one of the biggest racing fixtures in the calendar, I thought it fitting to offer some tips on who the runners and riders will be in the Tory leadership race.

First, don't waste your money on anyone who voted Remain in the EU referendum and has stuck to that position. Hostility towards Remainers in an already eurosceptic parliamentary party and membership is hardening with those who voted for Brexit regretful that Theresa May was entrusted with the divorce deal.

Now forced to hand over control of Brexit to parliament, it is but a matter of time before she has to stand down. But who replaces her is a wide and open field, with a dozen or more Tories thinking of running.

The eurosceptic wing of the parliamentary party is determined not to make that mistake again: One Nation Tories know it, which is why the poster-girl of that wing of the party Amber Rudd is likely to team up with a Brexiteer - could be Boris Johnson or Michael Gove - instead, bringing supporters in exchange for perhaps becoming Britain's first female chancellor.

The eurosceptic ERG parliamentary grouping already tried to oust May in December and are determined that their candidate makes it through to the final two. A voting block of 110 MPs or more, if the Brexiteers coalesce around one candidate, they will be the candidate to beat.

With that in mind an internal ERG hustings is a "live option" according to one senior figure which is being discussed. Whether the candidates would accept it is an entirely different matter given the number of MPs who fancy their chances.

It's worth putting a punt on Boris Johnson or Mr Raab as the front runners. While Mr Johnson is reviled by many on the Remainer side of the party, he commands support of the ERG chair Jacob Rees-Mogg and other senior Brexiteers, one of whom told me the other day that plenty of MPs will hold their nose and vote for Mr Johnson because he has - like him or loathe him - vote winning powers.

Michael Gove may also consider a run - although ERG-ers tell me he is not trusted in the parliamentary party after his betrayal of Mr Johnson in the 2016 run-off.

Former cabinet ministers David Davis and Esther McVey will also be mulling options, while rumours swirl that the runner-up in 2016 Andrea Leadsom is also planning to put her hat in the ring. Odds worsen for Brexiteers who have remained in government while others - Mr Johnson, Mr Raab and Ms McVey - have quit on principle. Mr Davis's decision to back Mrs May's deal on Tuesday night might also play against him, according to a rival Brexiteer.

My top two Brexiteers are Mr Johnson and Mr Raab. They will be battling it out with the two other front runners, Home Secretary Sajid Javid and Foreign Secretary Mr Hunt. This duo, who voted Remain in the referendum, have since positioned themselves as pragmatic Brexiteers. But they'll both want - need - the cover of a genuine Brexiteer (Mr Gove if he decides not to run himself, Penny Mordaunt, Liam Fox, Priti Patel) to improve their chances amongst eurosceptic party members.

Treasury minister Liz Truss and Defence Secretary Gavin Williamson too are in this grouping. I expect Ms Truss to make a run while Mr Williamson, a former whip who supported Mrs May in 2016, is more likely to lend his support to another candidate in order to lock in a good cabinet job.

Watch too for the dark horse health secretary Mr Hancock. One government source reckons he could ride straight through the middle in this packed field - I'd put him on as an outside bet.

The Tory party chair, Brandon Lewis, might also fancy his chances.

Then, if you want to take a punt, there are a number of outside bets who might have a canter out to show their pedigree for perhaps next time around if not this.

Tobias Ellwood, the defence minister, might have a go, as could Johnny Mercer, who has become one of the party's most prominent backbenchers since becoming an MP in 2015. Watch for deputy chairman James Cleverly and the chair of the foreign affairs select committee Tom Tugendhat too.

The starting gun hasn't been fired but there is plenty of jostling for position; prepare for your small screen to remain jam-packed with would-be successors for some weeks yet. This race is wide open and the field is crowded. Mrs May was anointed Conservative party leader in 2016, but next time is going to be one hell of a race.

Sky Views is a series of comment pieces by Sky News editors and correspondents, published every morning.

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