(AFP) - The race to become Britain's next premier has opened in earnest with an array of hopefuls promising to succeed where Theresa May failed and finally pull the divided country out of the EU.

But European leaders insisted they had made their final offer after months of acrimonious talks that produced an unpopular compromise for which May ended up paying with her job.

May is bowing out with her legacy in tatters and the country in agony over what to do about the voters' decision in 2016 to abandon the European integration project after nearly 50 years.

The markets view the risk of Britain crashing out of the EU bloc when the twice-delayed departure date arrives on October 31 as uncomfortably high.

Their main concern is that some of the current frontrunners to head May's Conservative Party say they will get Brexit done at any cost.

"We will leave the EU on October 31, deal or no deal," former foreign minister Boris Johnson said Friday in Switzerland.

Johnson's main challenges will come from former Brexit secretary Dominic Raab -- viewed as an even more committed eurosceptic -- and Foreign Secretary Jeremy Hunt.

Both declared their candidacies in the Sunday papers.

Raab wrote in The Mail on Sunday that "I would prefer that we leave with a deal".

But "we will not be taken seriously in Brussels unless we are clear that we will walk away on World Trade Organisation (WTO) terms, if the EU doesn't budge," Raab stressed.

Hunt had campaigned against Brexit in 2016 but has since reversed his stance.

"What matters is whether you believe in Brexit, not how you voted in 2016," he told The Sunday Times.

"We can never take no-deal off the table but the best way of avoiding it is to make sure you have someone who is capable of negotiating a deal," Britain's top diplomat said.

- 'Prepared to walk away' -

Former House of Commons leader Andrea Leadsom, whose resignation on Thursday pushed May towards stepping down, also confirmed she will run, telling The Sunday Times she would lead Britain out of the EU on October 31 with or without a deal.

"To succeed in a negotiation you have to be prepared to walk away," she told the paper, arguing she had the "experience and confidence" to "lead this country into a brighter future".

Brexit-backing Environment Secretary Michael Gove is also expected to throw his hat in the ring in a BBC interview to be aired on Sunday evening.

The contest is being held against the backdrop of European Parliament elections that the new Brexit Party of the anti-EU populist Nigel Farage is expected to win with about a third of the vote.

Polls indicate that the Conservatives will be punished for their bickering over Brexit and could finish as low as fifth -- their worst result in a national election.

The candidates are also mindful of a party revolt over May's fateful decision to court the pro-EU opposition with the promise of a second Brexit referendum.

The concession was designed to help ram her withdrawal agreement through parliament on the fourth attempt.

But it won her no converts and sparked a party coup attempt that forced May to walk away before she was pushed out.

This prompted more EU-friendly hopefuls such as Work and Pensions Secretary Amber Rudd to concede they stood no chance and would not vie for the job.

"I am conscious the Conservative Party wants someone who they believe is very enthusiastic about Brexit," Rudd told The Daily Telegraph.

Johnson is a popular figure viewed by many Conservatives as their best answer to Farage.

But a long political career that also saw him serve as London's mayor has made him enemies in parliament who will try to block his rise to the top.

- Dark horses -

Parliamentary party members will begin whittling down the field of contenders to a final two on June 10.

The finalists will then be put to a postal ballot of around 100,000 party members in July.

The field grew further on Saturday when Health Secretary Matt Hancock entered the race with a promise to take a more moderate approach.

Leaving the European Union without an agreement is "not an active policy choice that is available to the next prime minister," Hancock told Sky News.

Hancock is view as one of the dark horses who might make it through a crowded field of more than a dozen names.

International Development Secretary Rory Stewart is also positioning himself as a more consensus-seeking alternative to Johnson.

"It now seems that (Johnson) is coming out for a no-deal Brexit," Stewart told BBC radio.

"I think it would be a huge mistake. Damaging, unnecessary, and I think also dishonest."

Yet neither Hancock nor Stewart would say if they would push ahead with May's current agreement or try to secure added concessions from Brussels.

© Agence France-Presse