Taking part in the European elections is a further blow to May who, after securing a divorce deal with the EU in November, has been unable to implement the agreement and faces growing calls to bring forward her decision to stand down as prime minister.
It follows a request from the Tory 1922 committee for "clarity" on the issue.
Meanwhile, cross-party talks to break the Brexit deadlock resumed.
The Prime Minister can still guide the United Kingdom out of the European Union before then but is seemingly struggling to find support to be able to do that.
But they will last just till it becomes chronically embarrassing for each party that the fiction of a possible cross-party Brexit pact renders meaningless and fatuous all their campaigning in the European Union elections - which probably means the talks collapse at the end of the week.
Treasurer Sir Geoffrey Clifton-Brown said Mrs May should announce a "road map" for her resignation after the European elections, set for 23 May.
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However, while Labour will want to string out the talks, they will not want to join what Mr Farage has already branded "a coalition against the people" to help Mrs May's deal through.
In an unprecedented move, the National Conservative Convention - the most senior body within the voluntary party - is to hold a vote of confidence in her leadership next month.
"It's aimed at Conservative supporters who think the prime minister is doing her best to get this over..."
The Government has accepted it can not get its Brexit deal through Parliament in time to avoid European elections on May 23.
The government had previously set deadlines of 22 May and 30 June to get a withdrawal agreement over the line, but has now acknowledged that these dates could be unrealistic.
But Ms Long-Bailey said there had been no movement towards a customs union, temporary or otherwise, and would only say another referendum was "one of many options".
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