Media playback is unsupported on your device Media caption Theresa May denies Brexit deal is 'dead in the water'

Theresa May has been accused of "caving in" to Conservative Brexiteers after agreeing to their changes to a key piece of legislation.

Critics said accepting the amendments to the Customs Bill meant the prime minister's recently announced trade proposals were "dead in the water".

But Mrs May said this was "absolutely wrong" and that the changes were "consistent" with her plan.

The amendments relate to trading across UK-EU borders after Brexit.

The UK is due to leave the EU on 29 March 2019 but has yet to agree how its final relationship with the bloc will work.

After a meeting of the cabinet at Chequers, last week the government published a White Paper setting out its preferred trading relationship with the EU.

The proposals, including a "common rule book" between the two sides, have angered many Tory MPs. And they were set to show their displeasure by trying to amend the Taxation (Cross Border Trade) Bill, known as the Customs Bill.

What the amendments mean

Downing Street now says it will accept the four amendments - one of which could stop the UK from collecting tariffs for the EU, part of Theresa May's Chequers plan, unless the rest of the EU reciprocates.

Another change could make the EU's "backstop" on customs impossible by ruling out a border in the Irish Sea.

The other two amendments would ensure the UK was out of the EU's VAT regime and require new legislation if the government wanted to form a customs union with the EU.

Theresa May's spokesman said the changes were "consistent" with the proposals put forward by the government so far.

But Conservative MP Anna Soubry said the prime minister's Chequers plan had now been "wrecked by caving in to the hard, no-deal Brexiteers".

Another Tory MP, Heidi Allen, said the amendments "fundamentally undermine the Chequers proposal".

In the Commons, Labour MP Stephen Kinnock said the prime minister had "capitulated" to Conservative Brexiteers and that the proposals agreed at the Chequers summit were now "dead in the water".

Mrs May denied this, adding: "I would not have gone through all the work that I did to ensure that we reached that agreement only to see it changed in some way through these bills."

The government, which does not have a Commons majority, has been under pressure from MPs on both sides of the Brexit debate.

Tories clash in the Commons

Media playback is unsupported on your device Media caption Anna Soubry criticised colleagues who have a "gold-plated pension" and support Brexit

As news broke that the Brexiteers' amendments had been accepted, there were angry exchanges between Conservative MPs as the Customs Bill was debated.

Pro-EU Anna Soubry suggested backbench Eurosceptic Jacob Rees-Mogg was now "running Britain".

"This government is in grave danger of not just losing the plot but losing a considerable amount of support from the people of this country unless we get Brexit right," she said.

As Ms Soubry praised former prime minister Margaret Thatcher's support of free trade, she was told by former Tory minister Sir Edward Leigh that she "ain't no Margaret Thatcher".

"I don't pretend to be able to walk in Margaret Thatcher's boots," she responded.

Later, Ms Soubry said: "Nobody voted Leave on the basis that somebody with a gold-plated pension and inherited wealth would take their job away from them."

David Davis, who resigned as Brexit secretary in protest at the Chequers proposals, urged MPs to support the Customs Bill, describing it as "vital legislation".

Mr Davis said the EU was a "slow and not very effective negotiator of free trade agreements", and that the UK had a negotiating hand "over and above our economic weight".

Analysis by BBC business correspondent Jonty Bloom

The trouble with the tariffs amendment is that it seems to blow a hole in the government's policy of forming what it calls a Facilitated Customs Arrangement with the EU.

The plan was that the UK would collect EU tariffs on goods imported into the UK and pass them onto Brussels if the goods were destined for the EU, but British firms could get a rebate if the goods stayed in the UK.

It was messy, complicated and many thought it unworkable, but it was always assumed that the EU would not reciprocate - that they would not collect tariffs for the UK at their ports in return.

Insisting that they have to do so will be difficult if not impossible to get around.

Greening calls for referendum

Earlier Mr Davis said he still backed Theresa May, telling reporters as he left his London home that "my name's not Geoffrey Howe" - a reference to the late Conservative politician whose barbed criticisms of Margaret Thatcher during his resignation speech in 1990 paved the way for her subsequent downfall.

Scott Mann became the latest Tory MP to stand down as a ministerial aide to the Treasury in protest at the PM's plan, following Robert Courts who did the same on Sunday.

Former education secretary Justine Greening said the plan was the "worst of both worlds" as she became the most senior Tory politician to call for another referendum on the final deal to break the current "deadlock".