Theresa May is preparing to give MPs a vote on the key piece of legislation enacting Britain’s exit from the European Union next week, as negotiations with Labour continue.

The prime minister will discuss Brexit with her cabinet colleagues, with government sources suggesting one likely way forward is to table the withdrawal and implementation bill (WAB) in the next 10 days.

Downing Street continues to insist that it hopes to secure parliamentary ratification of a Brexit deal in time to avoid the UK having to participate in next month’s European parliament elections.

Bringing back the WAB, which parliament must pass in order to ratify May’s Brexit deal, would help to avoid the Speaker’s stricture that the government cannot hold another “meaningful vote” on an unchanged deal.

May’s official spokesman said: “Every day that parliament doesn’t ratify the withdrawal agreement, the harder it will be to avoid the European parliamentary elections, and the prime minister has made clear that she doesn’t believe it is in the country’s interests to take part in those elections.”

He said the government had spent a significant amount of time and work to get the bill ready.

Introducing it would be a high-stakes gamble unless the government is confident of securing considerably more support. May’s deal was rejected for a third time, by a majority of 58, last month.

If the WAB is rejected at its second reading – MPs’ second opportunity to vote on it – the government could not bring it back in the current parliamentary session.

As yet there is little sign that negotiations with Labour are close to yielding an agreement that could help shift the parliamentary numbers decisively.

The current parliamentary session had been expected to last two years instead of the usual one, to allow the government to pass all the legislation necessary for Brexit. May’s spokesman confirmed there were no plans to hold a Queen’s speech, marking the start of a new parliamentary term.

“The length of the parliamentary session is determined by the progress of legislation. Clearly we still have important legislation which needs passing,” he said.

Talks with Labour continued at official levels last week during MPs’ Easter break, but they are expected to resume in earnest on Tuesday, with May’s de facto deputy, David Lidington, the Brexit secretary, Steve Barclay, the chief whip, Julian Smith, and May’s chief of staff, Gavin Barwell, attending from the government side.

May’s spokesman said the prime minister could also join the talks at some point. “If there is a point where it would be helpful for the prime minister to hold further discussions with the leader of the opposition, she obviously stands ready to do so.”

Asked about whether the government was willing to contemplate a customs union to secure a deal with Labour, the spokesman said: “You know the prime minister’s position with regard to the importance of being able to do trade deals.

“We have said we approach these talks in a constructive manner,” he added. “If we are to agree a unified way forward, that would require compromise on both sides.”