London, May 15 (IANS): UK MPs will vote on a Brexit bill again in early June whether or not the government of Prime Minister Theresa May and the opposition Labour Party have reached a deal, a Downing Street spokesperson has said.

The spokesperson said on Tuesday night that a vote on the Withdrawal Agreement Bill that would pave the way for Brexit was "imperative" if the UK was to leave the European Union (EU) before the MPs' summer recess, reports the BBC.

However, this would not amount to a fourth so-called meaningful vote on the Prime Minister's Withdrawal Agreement itself.

UK needs to pass a law to implement the withdrawal agreement - the part of May's Brexit deal which will take the country out of the EU - in UK law.

This is a requirement under the terms of previous Brexit legislation passed last year.

The legislation would make the citizens' rights part of the agreement directly enforceable in UK courts, and set their relationship with the EU's Court of Justice.

Attempts to find a cross-party compromise began after May's Brexit deal was rejected three times by MPs.

The development comes after May and Labour leader Jeremy Corbyn met on Tuesday evening to discuss the ongoing talks, which the Downing Street gas described as "both useful and constructive", the BBC said.

May had made clear the government's "determination to bring the talks to a conclusion and deliver on the referendum result to leave the EU", it added.

Meawnhile, a Labour spokesman said Corbyn had "raised doubts over the credibility of government commitments, following statements by Conservative MPs and cabinet ministers seeking to replace the Prime Minister".

He also said that Corbyn had called for "further movement" from the government and that the Prime Minister's team had agreed to bring back "further proposals tomorrow (Wednesday)".

The UK had been due to leave the European Union on March 29, but the deadline was pushed to October 31 after Parliament was unable to agree a way forward.