No 10 has instead set a new deadline of the Commons summer recess, likely to be the end of the third or fourth week of July, to finalise Brexit and pass legislation, suggesting that they expect MEPs are all but certain to take their seats on July 2.
Foreign Secretary Jeremy Hunt has said that all sides in the cross-party Brexit talks between the Government and Labour need to be willing to compromise.
David Lidington, May's de facto deputy, said despite taking part in the elections to the European Parliament on May 23, there was still time to avoid those elected taking their seats.
So talks between government and Labour will fail.
It comes after a bad week for the two main parties in the local elections nationally where the Conservatives lost more than 1,300 councillors and Labour more than 80, viewed as a voter reaction against their failure to deliver Brexit.
The talks were given new urgency by last week's local elections in Britain, which saw the Conservatives hammered and Labour also lose ground as voters expressed anger at the Brexit mess.
Australian PM Morrison egged on election campaign trail
Mr Morrison helped the woman to her feet and spoke with her before she was created by St John Ambulance members at the scene. Australian Prime Minister Scott Morrison had a lucky escape after a protester tried and failed to crack an egg on his head.
Speculation is now increasing that the United Kingdom might be facing an inevitable second referendum.
Sir Graham Brady, the chairman of the influential 199 Committee, "will be sent straight back to see her" if he returns from a meeting with the Prime Minister today without a clear idea of when she will call it a day.
May and her aides reportedly discussed giving the electorate a three-way vote on whether to take Brexit with a deal, leave without a deal, or remain.
Jeremy Corbyn will pay a visit to the county this week to launch the Labour manifesto for the European elections.
But with both parties, like much of the country, deeply divided over Brexit, any breakthrough from Tuesday's talks might be hard to come by.
Labour sources were dismissive of weekend reports the government would offer new concessions, including a temporary customs union with the EU until a national election due in June 2022, saying such a proposal would not go far enough.
"I want to look at whatever deal is come to between the parties and I know this is a crucial week", he told BBC radio.