LONDON (Reuters) - Britain’s opposition Labour Party is moving closer to supporting a second Brexit referendum and could do so as soon as this week, several of its senior lawmakers said on Sunday.

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With just over a month until Britain is due to leave the bloc on March 29, Prime Minister Theresa May is still seeking to negotiate changes to her Brexit deal with Brussels in order to secure the backing of parliament for it.

Labour leader Jeremy Corbyn has so far stuck to Labour policy to keep the option of a second referendum “on the table” if May’s government fails to secure a deal with Brussels that can break an impasse in parliament, preferring a new election or his own proposed deal.

May has promised parliament the opportunity to vote on the next steps on Brexit on Feb. 27 and lawmakers intend to put forward a series of proposed changes, or amendments, to her plan, including one saying it should be put to a referendum.

Asked whether this would be the week Labour comes out in support of a second referendum, the party’s deputy leader Tom Watson told BBC TV: “It might be ... We are getting closer to that point.”

“We are heading in that direction but there is still more play in the day’s ahead,” he said.

Labour finance spokesman John McDonnell made similar comments in an interview with BBC Radio, while the party’s trade spokesman Barry Gardiner told Sky News the idea of a second vote would become more important as a “safety net” as Britain edged closer to leaving without a deal.

Any public vote could not include May’s deal as one of the options however as it was “not credible”, he said.

The prospect of holding a second referendum poses a dilemma for Corbyn: while many of the party’s members fervently back a so-called People’s Vote, others just want Britain to leave as soon as possible.

McDonnell said he had met with two Labour lawmakers, Peter Kyle and Phil Wilson, who have proposed May’s deal be put to the public in another referendum but he did not think enough Labour lawmakers would want to vote for it as it stands because it would involve backing May’s Brexit agreement.

“We’re working with them to see can we have a redraft of that amendment which people could vote for. I think there’s a high possibility we could,” he said.

“There’s increasingly large numbers of people who will consider now moving toward a public vote situation to block a no deal, and to block a bad deal, that Theresa May’s deal is – that will be the vote of this coming week.”

Labour lawmaker Wilson told The Sunday Times newspaper he had also held talks with some of May’s ministers to gain their backing for his second referendum amendment.