London (CNN) On Friday, the United Kingdom missed its second Brexit deadline. By accepting the European Union's offer to remain until October 31, Theresa May all but guaranteed that the UK, which voted to leave the EU nearly three years ago, will participate in the European parliamentary elections next month .

The UK's inability to leave the EU on time is already impacting British and European politics.

On the same day that Brexit didn't happen (for the second time), Nigel Farage, the former leader of the anti-EU UKIP, launched his new political movement, the Brexit Party.

Farage, a Member of the European Parliament since 1999, says his party would target voters across the political spectrum who have been "betrayed" by the political class. He is placing a £1,000 ($1,300) bet on the Brexit Party winning the European elections and says that there will be "no more Mr. Nice Guy" on the campaign battlefield.

Farage knows a thing or two about European elections. In 2014, he led his former party to victory in the UK. European elections have notoriously low turnout, which can work in the favor of more radical politicians chasing the protest vote. In 2014, this meant UKIP, a party without a single seat in the UK Parliament, sent more MEPs to Brussels than any mainstream party.

This time, Farage will be able to use the single most divisive issue in the country to his advantage. Even if his party isn't as successful as he hopes, it's likely that a large chunk of the MEPs the UK sends will be euroskeptic.

This should worry the EU. As a full member state, the UK will have voting rights and be able to frustrate the EU's plans as long as it remains inside the bloc.

Jacob Rees-Mogg, a Conservative MP and leader of the pro-Brexit European Research Group, says this belligerent behavior is entirely justifiable and necessary.

"The EU has not been sincerely cooperative during the Brexit process, so I don't think we owe a duty of cooperation to the EU in return," Rees-Mogg said.

The EU has not been sincerely cooperative during the Brexit process, so I don't think we owe a duty of cooperation to the EU in return. Jacob Rees-Mogg

"If we do send euroskeptic MEPs to Brussels, I don't expect them to cooperate with federalist EU schemes and they should block any attempts to increase the EU's budget."

This uncomfortable reality is dawning on Europeans.

Marietje Schaake, a liberal member of the European Parliament, says key decisions will be made before October, including the election of a new EU Commission President.

"MEPs from the UK would have a vote on those. Similarly, the Brexit party will undoubtedly use every opportunity it has to negatively impact the EU, thereby clearly proving that contrary to its slogans, a seat at the table gives more influence than stepping away from it," Schaake said.

The Brexit failure is also affecting domestic politics in London. Having spent two years trying to get both hardline Brexiteer members of her own party and the Northern Irish Democratic Unionist Party on board with her plans, May last week gave up and started negotiating with the opposition Labour Party.

With both camps so divided on the Brexit question, any compromise would lead to chaos among both parties' MPs.

Some Labour MPs want Corbyn to push for a second referendum, meaning that they will approve May's deal, but on the condition that a public vote is then held. Even on that question, there is division on whether that vote should include the option to scrap Brexit altogether.

Labour's official Brexit position is that the UK remains in a permanent customs union with the EU. That wouldn't only infuriate Conservative backbenchers, but members of May's government.

Liam Fox, the UK's trade secretary, wrote that a customs union would leave the UK "stuck in the worst of both worlds, not only unable to set our international trade policy but subject, without representation, to the policy of an entity over which MPs would have no democratic control."

It would also be unpopular among leave-supporting Labour MPs.

Kate Hoey, a Labour MP who campaigned for Brexit, says "any Labour government that signs up to the customs union would not be able to deliver radical policies like using state aid or nationalization. I do not see any customs union compromise that doesn't break the promises in either parties' 2017 manifestos."

Few in London expect the talks between the two parties to go anywhere. May has already said that if her deal passes, she will resign, thus cementing her political legacy as the prime minister that managed to take the UK out of the EU. But eager as she might be to see Brexit off once and for all, doing so at the cost of leaving her party a divided mess would be rash.

Add to this the fact that the Labour Party can smell blood and has been in campaign mode for months. Why would it suddenly risk its credibility by bailing out a weak, Conservative government in May's final days as leader?

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While ex-UKIP leader Farage and others might still be hopeful of a pure, clean Brexit, the impasse has also lit a fire under Remain factions in the UK.

"It's April 29 and Britain hasn't left the European Union. Brexit is defeating itself," Wes Streeting, a pro-EU Labour MP told me earlier this week.

He says the campaign for a second referendum is in a far stronger position than many believed it ever could be.

"The PM has tried stoically to deliver on the outcome of the referendum, but she's found it impossible to deliver on the promises that were made to people during the referendum."

In Brussels, European diplomats and EU officials have been discussing the growing sense that Brexit might be evaporating. It's a view shared by the group campaigning for a second referendum.

Tom Brufatto, head of campaigns for the People's Vote, thinks that getting past March 29 was a "sigh of relief for a majority of people in the UK. The risk of no deal on a fixed date was causing a lot of anxiety of stress."

It provided Remain supporters with solid proof that leaving the EU was not the inevitable conclusion of this process.

I think there will be a mobilization of voters who want to take part in what will be the most important and high-profile election in the history of the European Union Tom Brufatto

"The extension was seen as a beacon hope," he said. "I think there will be a mobilization of voters who want to take part in what will be the most important and high-profile election in the history of the European Union."

The truth is that UK parliament's failure to agree on any Brexit outcome, combined with the EU's reluctance to kick the UK out, has left all options on the table. And the fact that there is no majority for anything in the House of Commons, while frustrating the Brexit process, means that whoever manages to break the deadlock first will likely win the day.

Whether that's hardline Brexiteers forcing May out of office and replacing her with a firebreather, Remainers getting a second referendum or May pulling off the impossible and striking a deal with Labour is anyone's guess.

The EU has given Britain breathing space to sort itself out. Its attempt to restore some semblance of calm to the Brexit process could lead to some of the bloodiest political battles yet.