Brussels last night warned that whoever replaces Theresa May would not be able to make changes to her Brexit deal.
And EU leaders, officials and diplomats all agreed that the chances of a No Deal Brexit had now dramatically increased.
The stage is now set for a showdown if Boris Johnson or another hardline Brexiteer, such as Dominic Raab, wins the keys to Number 10.
Her voice cracking, Mrs May said it had been the ‘honour of my life’ to be PM, and she hoped she would not be the last woman to lead the country
Guy Verhofstadt, who heads negotiations for the European Parliament, threw down the gauntlet to Mr Johnson and told the Daily Mail: ‘He is famous across Europe for making promises during the Brexit referendum that were undeliverable.
In the running: Boris Johnson split from his wife Marina and is in a relationship with former Conservative staffer Carrie Symonds
‘The current withdrawal agreement remains the only deal on the table. Why it remains blocked is a matter for the British people and their elected representatives.’
A spokesman for EU Commission president Jean-Claude Juncker said ‘there is no change’ to Brussels’s position and Dutch prime minister Mark Rutte said ‘the withdrawal agreement is not up for renegotiation’ adding that Mrs May’s resignation had ‘increased rather than decreased’ uncertainty.
Irish prime minister Leo Varadkar said: ‘This is a period of danger for us, but whatever happens we’re going to make sure that we hold our nerve.
‘In the next few months we could see the election of a hardline Eurosceptic prime minister who wants to repudiate the withdrawal agreement and go for No Deal or we may even see a new British government that wants to see a closer relationship with the EU and possibly even a second referendum.’
The Mays left Downing Street via the back door after she made her dramatic departure announcement today
His deputy, Simon Coveney, added: ‘Regardless of who the British Prime Minister is, the EU position will remain that the withdrawal agreement took two-and-a-half years to negotiate, and it’s closed.’
In the running: Dominic Raab has become a cheerleader for a hard Brexit since stepping down as Brexit secretary in November
But Spanish government spokesman Isabel Celaa warned that ‘a hard Brexit appears to be a reality that is near impossible to stop’.
She added that the UK Government and MPs would be ‘solely responsible for a No Deal exit and its consequences’.
EU diplomats said they most feared a hardline Brexiteer taking over, but predicted that if one did they would be broken down by Brussels.
One said: ‘I think the new PM, if everyone tells them what No Deal means, will be concerned with the ramifications.
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‘Everybody is afraid of Johnson because with him you never know what you get. Raab is utterly disliked because he is not honest, people don’t regard him as being honest.
‘Boris Johnson, he is difficult to estimate, because he’s such a populist but you don’t know if it’s words. Does he mean it? What’s behind what he says? Does he have a sense of responsibility or not?’
However, No Deal is not inevitable and depends on who the new prime minister is and when they first go to Brussels.
The drawn-out Tory leadership contest means Mrs May’s successor will not be in post until late July and will miss a key EU summit next month.
They may not even be in place until after Parliament’s summer recess begins on July 24, with MPs not coming back until September 4.
The next Brexit summit is on October 17, just two weeks before Britain is due to cut ties with the EU .Another option in that case would be for a second extension.
One EU source said: ‘I think there will be another extension because there will not have been enough time in office.
Philip May (pictured centre) looked as though he was suppressing an urge to comfort his wife as she made her speech. After her notorious coughing conference speech in 2017 he leapt on stage to embrace her at the end
In the running: Jeremy Hunt, a born-again Brexiteer after supporting Remain, toured Africa last month with wife Lucia
‘So whatever happens with Brexit, it will happen in 2020 and not in 2019 – that’s if the new prime minister isn’t completely intent on No Deal.’
Brussels is also preparing for the possibility of Mrs May’s successor calling a General Election. An extension would almost certainly be granted in such a scenario.
In the running: Michael Gove has made a remarkable political comeback after being sacked by Theresa May in 2016
Mrs May will meet EU leaders in Brussels on Tuesday for an informal summit dinner following the European Parliament elections. They will also discuss who should replace Mr Juncker and EU Council president Donald Tusk when their terms end in November.
Yesterday EU leaders paid tribute to Mrs May’s ‘tenacity, her courage and her determination’.
The EU’s chief Brexit negotiator Michel Barnier said: ‘I just want to express my full respect for Theresa May and for her determination in working towards an orderly withdrawal of the UK from the EU, and on our side we will work exactly in that direction in the next few weeks and months.’
Mr Juncker’s spokesman said: ‘President Juncker followed Prime Minister May’s announcement this morning without personal joy. Theresa May is a woman of courage for whom he has great respect.’
German Chancellor Angela Merkel said she had ‘respect’ for Mrs May and that she had ‘worked well’ with her.
Mr Varadkar said: ‘Politicians throughout the EU have admired her tenacity, her courage, and her determination during what has been a difficult and challenging time.’
Mr Rutte phoned Mrs May after her resignation speech. He said: ‘I told her that I thought what she did in the past years was brave and that she worked under incredibly difficult circumstances.’