LONDON (Reuters) - Britain’s two main parties set the stage on Monday for a battle over a no-deal Brexit, hoping to win back voters who abandoned them for a new movement led by eurosceptic Nigel Farage and other smaller parties in European elections.

After a punishing night when acrimonious divisions over Britain’s departure from the European Union were plain to see, contenders for the leadership of the governing Conservatives said the results were a demand to deliver Brexit no matter what.

Taking a different tack, the opposition Labour Party said a public vote - a new national election or second referendum - was the way to reunite the country. It pledged to make sure any new eurosceptic Conservative leader would not take Britain out of the EU without a transition deal to help protect the economy.

But with Farage’s Brexit Party, which prefers a no-deal Brexit, capturing the greatest number of votes for seats in the European Parliament, closely shadowed by a group of fervently pro-EU parties, Conservatives and Labour were under pressure to commit clearly to either side of the debate.

Almost three years since Britain voted narrowly to leave the EU and barely two months after the originally planned departure date, lawmakers remain at loggerheads over how, when or even whether the country will quit the club it joined in 1973.

For the Conservatives, who will name a new leader by the end of July, many of the would-be successors see the European vote outcome as proof they must seek a cleaner break with the EU, with several saying they would leave without a deal - a move some senior pro-EU Conservatives regard as foolhardy.

For Labour leader Jeremy Corbyn, pressure will mount to embrace a second referendum without qualification - something he has said would be needed to prevent a no-deal Brexit.

But what is clear from a vote which many used as a protest is that Brexit - which forced Prime Minister Theresa May to say she will resign on June 7 after failing to deliver Britain’s departure - risks shattering the election prospects of both the main parties.

Former foreign minister Boris Johnson, the favourite to replace May as party leader and prime minister, said the election message was “if we go on like this, we will be fired”.

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“We can and must deliver. No one sensible would aim exclusively for a no-deal outcome. No one responsible would take no-deal off the table,” Johnson, who was also London mayor, said in his regular column in the Telegraph newspaper.

“If we are courageous and optimistic, we can strike a good bargain with our friends across the Channel, come out well and on time - by October 31.”

Interior minister Sajid Javid became the ninth Conservative to declare he would run for the leadership, saying on Monday “first and foremost, we must deliver Brexit”.

NO DEAL

Javid was one of several prime ministerial contenders to express their belief that the disappointing result in the European vote, which put the Conservatives in fifth position, amounted to a clear demand for Britain to get on with Brexit. May said the results showed the importance of a negotiated deal.

The question posed for the Labour Party was a little different. With part of its support bolting to the Brexit Party and part to the pro-EU Liberal Democrats, who support a second Brexit referendum, some felt the pressure to change tack.

Labour’s finance chief, John McDonnell, caused a short-lived sensation in seeming to signal a shift in Labour policy to unequivocally backing a second referendum - something favoured by many party members but fought off by the party leadership.

But Corbyn sought to set the record straight, again saying Labour would do its utmost to stop a no-deal Brexit - something experts say might be legally trickier than many lawmakers earlier thought if faced with a eurosceptic prime minister determined to leave the EU by the current deadline of Oct. 31.

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“This issue will have to go back to the people, whether through a general election or a public vote,” Corbyn said in a statement.

After May announced on Friday that she was stepping down, many of her would-be successors have said they wanted Brexit with or without a deal, rejecting another public vote.

That response seemed to be a direct challenge to Farage, a former commodities broker whose campaigning helped force May’s predecessor, David Cameron, to stage the 2016 EU referendum.

After the Brexit Party came out on top in Sunday’s European vote with 31.6% of the vote, the 55-year-old Farage said on Monday he wanted to be included in any new negotiation to leave the EU.

But while the Brexit Party came first, with Farage’s former UKIP adding 3.3% of the vote, three staunchly pro-EU parties - the Liberal Democrats, Greens and Change UK - combined for 35.8%.

“Far from providing a clear verdict, the result simply underlined how difficult it is likely to be to find any outcome to the Brexit process that satisfies a clear majority of voters,” said John Curtice, a leading polling expert.