European Council president Donald Tusk said the Prime Minister told him during talks at No 10 last week it was “quite likely” she would be ready to trigger Article 50 of the Lisbon Treaty “maybe in January, maybe in February” 2017.
But a Downing Street source said Mrs May did not specifically mention January or February at the meeting and that Mr Tusk’s comments were an interpretation of their conversation.
The PM “recognises the need to deliver on the public verdict without delay”, the source added.
With Britain’s withdrawal clouded in confusion and no clear signal on whether the country intends to stay in the single market or not, Europe’s 27 other leaders gathered on Friday for an informal summit in the Slovakian capital, Bratislava, without the PM.
Speaking about his meeting with Mrs May, Mr Tusk told a summit press conference: “Prime Minister May was very open and honest with me.
“She declared that it’s almost impossible to trigger Article 50 this year but it’s quite likely that they will be ready maybe in January maybe in February next year.”
Formal negotiations between the UK and the EU cannot begin until she starts the two-year process, which Brexit Secretary David Davis has insisted will be triggered without a parliamentary vote.
Meanwhile, Defence Secretary Sir Michael Fallon vowed to block any proposals for an EU army while Britain remains a member of the union, in a move likely to anger European leaders.
In his state of the union address on Wednesday, European Commission president Jean-Claude Juncker called for EU countries “to pool their defence capabilities in the form of a permanent structured co-operation”, and proposed a European Defence Fund by the end of the year.
But Sir Michael said the UK would veto plans for any EU army that may rival Nato, as long as the country remained a member of the union.
“That is not going to happen,” he told The Times. “We are full members of the EU and we will go on resisting any attempt to set up a rival to Nato.
“We have always been concerned about unnecessarily duplicating what we already have in Nato.”
But former Liberal Democrat leader Lord (Menzies) Campbell said there was nothing the UK can do after Brexit to protect Nato from the potentially damaging effect of an EU army because it will not be able to veto its creation from outside the union.
The peer, who is a member of the UK parliamentary delegation to the Nato Assembly, said: “Even as a fervent European, I regard the creation of a European army as a deeply damaging, long-term threat to Nato.
“The cornerstone of European defence is Nato, of which the United States is the most senior partner contributing 75% of the budget of the alliance.
“The creation of a European army will only encourage isolationists in the United States to argue that Europe should be responsible for its own defence.
“At a time when few of the Nato countries can meet the minimum requirement of 2% of GDP defence expenditure, parallel headquarters and staff make no sense whatsoever. ”
In Bratislava, Mr Juncker insisted Britain cannot get access to the European single market without accepting the free movement of workers.
The conundrum has become central to the Brexit debate and has caused friction within the Government as ministers weigh up how to maintain the benefits of the trading bloc while regaining full control of the UK’s borders – a goal deemed by Mrs May as essential to properly implement the referendum result.
Mr Juncker said: “There’s a clear interlink as we made clear since the very beginning between the access to the internal market and the basic principles of the internal market, mainly the one of the freedom of movement of workers.
“We are sticking to that position and this is not a game between prime ministers leaving and prime ministers remaining, this is about people in Europe.
“It’s about the rights of ordinary people and workers, of those living in Europe, and so I can’t see any possibility of compromising on that very issue.”