A commitment that there will be no “physical infrastructure, including border posts, or checks and controls” in Northern Ireland has effectively killed a no deal scenario with the EU, MPs have heard.

Brexit Secretary David Davis’ decision to include the provision in the EU (Withdrawal) Bill has also made the maximum facilitation or “max fac” option — which would see new technology used to deal with cross-border trade — “unlawful”.

Tory Remainers and Labour’s shadow Brexit secretary Sir Keir Starmer, debating the Brexit bill for a second day in the Commons, said the inclusion of the Northern Ireland amendment meant the only option was to now “reproduce the customs union and the single market”.

Sir Keir said: “If maximum facilitation does involve infrastructure checks or controls, it would be unlawful under the provision passed yesterday, therefore it cannot happen.

“The only answer to no hard border in Northern Ireland in the end is a customs union and high levels of market alignment, the fact that was accepted by the Government and turned into domestic law gives it a status it didn’t have until yesterday.”

Tory MP Heidi Allen (South Cambridgeshire) responded to his point, saying: “It’s huge, it actually says I think logically we will have to come to a customs union agreement, partnership, love dance, don’t care what you call it, that’s what we will need to avoid any border to Northern Ireland.”

Former attorney general Dominic Grieve also agreed, saying: “Not only will we have to stay in a form of customs arrangement amounting to a union, but we’re also going to have to have a high level of regulatory alignment because otherwise the life that takes place along the border will be impossible because of different regulations on either side.”

Tory grandee Ken Clarke said: “It was the most significant thing that happened yesterday, but in the cirtus that surrounded everything and the timetable stopped us debating it nobody.

“The legally binding commitment yesterday extends the needs of the Irish border to the whole of the United Kingdom.

“So we’re talking about Dover and we’re not having a border down the Irish Sea so the United Kingdom has got to negotiate an arrangement with the EU as a whole, which has no new frontier barriers.

“So effectively we are going to reproduce the customs union and the single market and the Government will not be able to comply with Tuesday’s legal obligation unless it does so.”

Solicitor General Robert Buckland later said leaving with a no deal and trading under World Trade Organisation rules would be inconsistent with Government policy on the Northern Ireland border.

It followed a question from Labour’s Chuka Umunna (Streatham), who asked: “Does he accept that if we were to leave with no deal and we were trading on WTO rules, that under WTO rules would necessitate a border, therefore leaving with no deal is inconsistent with Government policy as he has just stated it?”

Mr Buckland replied: “I entirely agree: the Government’s policy is to achieve a deal because we are mindful of the points that he and others understand.”

Tory MP Mr Grieve later confirmed he would rebel against the Government by supporting the Lords EEA amendment, telling the Commons: “There becomes a point when you have to stand up and be counted, and if it’s not this week it has to be next week.

“The truth is I’m really anxious for my constituents, really anxious for the direction of travel that we are taking generally: I respect the decision in the referendum but we are closing off options of how we conduct future relationships in ways which are utterly damaging to ourselves.”

Mr Grieve acknowledged the EEA amendment is “rather flawed” but that it also has merit before saying Labour’s proposal was a “motherhood and apple pie” amendment which he could not support.

Yvette Cooper, Labour chairwoman of the Home Affairs Select Committee, warned against a “Dad’s Army version of Brexit” and said the UK is in danger of “turning ourselves into a national joke” by not focusing on the real issues.

Ms Cooper added she believes there is a majority across the country and Government in favour of a “close economic relationship”, which means some version of single market participation – or as close as the UK can get to it.

Ms Allen, in her speech, urged the Government to develop a lifeboat plan B by negotiating continued access to the EEA along with joining Efta.

The MP, who said she would be abstaining, said: “It is far inferior to a bespoke customs arrangement that the Prime Minister is determined to seek, but if she doesn’t we need it as a plan B.”

Ms Allen added: “The majority in this House and the British public do not want no deal, no lifeboat either – it’d be absolutely economic suicide.”

She argued against ruling out her suggested plan B, noting: “We’d be absolute fools to write it off. So let’s get to the Trade Bill, see where we are, see how the June council goes and potentially that might be the lifeboat we all should grasp with both hands.”

A Department for Exiting the European Union spokesman said: “We have made clear our commitment to avoiding a hard border between Northern Ireland and Ireland, as well as avoiding any borders within our United Kingdom.

“The Lords amendment only relates to how we use some of the powers in the EU (Withdrawal) Bill and does not have any wider effect.

“We are confident that we will secure a deal which works for the UK and the EU, including Ireland.”