Cabinet ministers are personally trying to convince wavering Tory MPs to back Theresa May’s Brexit deal in a last-ditch attempt to avoid defeat in Tuesday’s crunch vote.

Chief Whip Julian Smith and his team normally take control of efforts to cajole MPs into backing government policy.

But the prime minister’s top team have launched a charm offensive with backbenchers they have a personal relationship with to try to reverse opposition to the under-fire Brexit deal ahead of Tuesday’s momentous vote, a Whitehall source said.

Commons Leader Andrea Leadsom is understood to be among those leading the effort, calling in MPs for one-to-one chats over cups of tea in her office in parliament, but other ministers are also involved.

May on Tuesday admitted to her cabinet that she may lose the vote but the margin of defeat could be crucial, with a margin more than 100 votes seen as potentially fatal for her deal.

The whipping effort also comes as May suffered her second defeat on Brexit at the hands of anti no-deal MPs in the space of 24 hours.

In another signal of the effort the government is making to try to win over MPs, Brexit Secretary Stephen Barclay accepted backbench plans for a parliamentary lock on entering the Irish border backstop, which is causing the most opposition to the deal.

The government will accept an amendment from Tory former minister Sir Hugo Swire which requires the government to secure parliamentary approval to either extend the Brexit transition period or trigger the backstop if no trade deal is concluded by the end of 2020.

The amendment also states the government should obtain “further assurance” from the EU that the backstop would only be temporary and that the UK and Brussels would intend to agree a free trade deal within a year of it coming into force to supersede it.

Opening the Brexit debate in the Commons, Barclay however admitted: “I recognise that that alone will not be sufficient for all of the concerns that colleagues may have, but I think it is a welcome step forward.”

The backstop is intended to act as a safety net to avoid a hard border on the island of Ireland, and would give Northern Ireland continued access to the single market – with Brussels rules applying in many circumstances – and create a customs union for the whole UK with the EU.

MPs are concerned that Britain could become trapped in the arrangement permanently, unable to sign free trade deals with other countries around the world.

Conservative former minister David Jones described the backstop as the “most repugnant” element of the deal and reiterated Brexiteers’ dismissal of anything that falls short of a rewriting of the backstop in the Brexit deal, which the EU is not currently offering.

“What is needed is a re-wording of the withdrawal agreement,” Jones.

The DUP’s Brexit spokesman Sammy Wilson said the agreement in fact placed the Belfast Agreement, which brought peace to Northern Ireland, “in jeopardy”.

He said: “The withdrawal agreement and especially the backstop arrangement which actually forcibly would remove Northern Ireland from the rest of the United Kingdom, laws made in Brussels rather than Westminster, the Northern Ireland economy cut off from trade deals which the United Kingdom would enter into with the rest of the world. That has put in jeopardy the fine balance that which there was in the Belfast Agreement.”

Tory former minister Jo Johnson later intervened to accuse the government of peddling “fantasy”, saying: “There is no chance at all of us concluding a trade deal with the EU by 2020, very little chance of doing so by 2022, a far more realistic prospect is we might do so by the mid-2020s.”

Shadow Brexit secretary Sir Keir Starmer told the Commons “nothing had changed” with May’s deal despite a month’s delay.

He said: “They were of course challenged on the basis this was just a way of delaying, avoiding a humiliating defeat, they were just running down the clock.

“Now, 30 days on, those rebuttals rung hollow.

“The prime minister is often mocked for saying ‘nothing has changed’, but this time nothing has changed.”