MPs may not be given a vote on a revised version of Theresa May’s Brexit deal this month, a minister has said.
James Brokenshire said there might be another series of non-binding votes on possible Brexit alternatives instead.
The prime minister has to get an agreement with the EU passed by MPs by 29 March to avoid a no-deal Brexit.
She will ask MPs for more time to get changes to the deal in talks with Brussels – but Labour has accused her of “cynically” running down the clock.
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Labour is proposing its own Brexit plan, which would involve the UK staying in a customs union with the EU, which they say could get the backing of a majority of MPs.
The government has not ruled out supporting this – and has promised a formal response to it and further talks with Labour – but they say it would prevent the UK from making its own trade deals after Brexit.
On Wednesday, Mrs May will ask MPs for more time to get legally-binding changes to the controversial Northern Irish backstop, which she believes will be enough to secure a majority in Parliament for her deal.
But Labour’s shadow Brexit secretary, Sir Keir Starmer, says he believes the prime minister is “pretending to make progress” on this issue.
He says what she actually intends to do is return to Parliament after the 21/22 March European Council summit the week before Brexit and offer MPs a “binary choice” – her deal or no deal.
“We can’t allow that to happen,” Sir Keir told The Sunday Times.
“There needs to be a day when Parliament says that’s it, enough is enough.”
On Thursday, Labour will attempt to force the government to hold the final, “meaningful vote” on Mrs May’s Brexit deal by 26 February.
Housing and Communities Secretary Mr Brokenshire refused to commit to this in an interview with the BBC’s Andrew Marr Show, saying there could be more votes on amendments to the proposed deal instead.
“If the meaningful vote has not happened, so in other words things have not concluded, then Parliament would have that further opportunity by no later than 27 February,” said Mr Brokenshire.
“I think that gives that sense of timetable, clarity and purpose on what we are doing with the EU – taking that work forward and our determination to get a deal – but equally knowing that role that Parliament very firmly has.”
Other options likely to be debated by MPs on Thursday – include extending Article 50, the legal mechanism taking the UK out of the EU on 29 March, to allow more time to reach an agreement with Brussels.
There are fewer than 50 days until Brexit. The law is already in place which means the UK will leave the EU on 29 March 2019.
Mrs May’s Brexit deal – which she spent months negotiating and had agreed with the EU – covers the terms of the UK’s divorce and the framework of future relations.
But it was rejected by the UK Parliament and if it is not approved by Brexit day, the default position would be a no-deal Brexit.
Last month, Parliament voted in favour of an amendment that supported most of the PM’s deal but called for backstop – which is a last-resort option to prevent a hard border in Ireland – to be replaced with “alternative arrangements”. The prime minister is now in talks with Brussels to seek these changes to the backstop.
A number of government ministers will also be meeting their counterparts across the continent this week, in order to underline Mrs May’s determination to achieve a deal.
Meanwhile, former Prime Minister Tony Blair – who wanted the UK to stay in the EU – has told Sky News that a no-deal exit could be “devastating” for Northern Ireland’s peace process.
He told the Sophy Ridge on Sunday programme that it would lead to a “very hard border” on the island of Ireland and is contrary to the Good Friday Agreement, the peace deal he helped negotiate which brought an end to The Troubles.
Critics of the backstop in Mrs May’s current deal say they could tie the UK to EU rules indefinitely or mean Northern Ireland ends up under a different system to the rest of the UK.
But the Irish government and the EU have repeatedly rejected calls for changes.