Housing minister James Brokenshire confirmed May's plans to the BBC: "The government will commit that the meaningful vote - the deal coming back - has not happened by 27 February, then we will allow a further motion, voteable in parliament, to take place, to give that sense of assurance as to the process moving forward".
"We can't allow that to happen", Starmer said. While UK PM May's comment might appear to sooth an ongoing drama over Brussels, the European Union leaders had asked for insurance for Northern Irish borders, which appeared to be complicating the overall complexion of the recent round of talks.
May is due to report back to parliament on her negotiations with the European Union on 13 February, a few weeks after she secured MPs' support to go back to Brussels.
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 United Kingdom from making its own trade deals after Brexit.
In the vote this week lawmakers are set to vote on amendments that could limit May's options and give parliament a broader say over the Brexit process.
May will promise lawmakers a second opportunity to influence the Brexit talks later in the month in a bid to stave off any rebellion from within her own party by those who fear Britain could end up leaving without a deal.
"We would have a hard border, a very hard border, no-deal Brexit means a really hard border between the north and south of Ireland".
The former PM said crashing out of the European Union would inevitably lead to a "really hard border" on the island of Ireland and cause a huge split within the UK.
May to appeal for more time to secure backstop changes
Tony Blair stepped up his warnings on no-deal Brexit today saying it would be "devastating" for Northern Ireland and breach the Good Friday Agreement.
The PM is facing another round of crunch Brexit votes in the Commons on Valentine's Day - with Remainer and Eurosceptic opponents again seeking to bind her hands.
May is seeking changes to her deal with Brussels after it was rejected by a record majority in parliament on January 15.
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".
May held talks in Brussels last week in an attempt to secure changes to the Northern Ireland backstop as demanded by Tory MPs.
The EU and the Irish Government have insisted that the backstop is the best way of guaranteeing there will be no hard border in Ireland.
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.
Tony Blair has become the latest person to weigh in on the possibility of a no-deal Brexit, claiming that the consequences of it would be "devastating" for Northern Ireland.
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