British Prime Minister Theresa May leaves 10 Downing Street to makes her way to the Parliament as she attends Prime Minister Questions session (PMQs), London on July 4, 2018. (Photo by Alberto Pezzali/NurPhoto via Getty Images)

Prime Minister Theresa May bowed to pressure from Brexit supporters in her governing Conservative Party on Monday, accepting their changes to a customs bill that underpins Britain's departure from the European Union.

May, vulnerable in parliament after losing her party's majority at an ill-judged election last year, has come under fire from both wings of her party over a hard-won Brexit plan, with one ex-minister calling it the "worst of all worlds."

Eurosceptic lawmakers had targeted her government's customs legislation to try to toughen up her plans to leave the EU, but instead of facing them down and fueling tensions, her spokesman said the government would accept their four amendments.

It was not clear the move would fundamentally change her plans - the changes do little more than to put government policy into law, her spokesman said - but it was a victory of sorts for those lawmakers who say May has betrayed them on Brexit, the biggest shift in British trade and foreign policy for decades.

"We will be accepting those four amendments," the spokesman told reporters, saying the government believed they were "consistent" with the white paper policy document ministers agreed earlier this month.

"We have accepted these amendments because we believe them to be consistent with the approach that was set out and agreed at Chequers," he said.

May had to fight hard to get the agreement of cabinet ministers at her Chequers country residence for her vision for Britain's future ties with the EU, only for it to be undermined by the resignations last week of her Brexit minister David Davis and foreign secretary Boris Johnson.

The plan, only a starting point for the second phase of talks with the EU, has come under fire from other eurosceptic lawmakers, who say the proposal to keep close customs ties to the EU betrays her commitment for a clean break with the bloc.

The battle over the amendments to the Taxation (Cross-border Trade) Bill, or customs bill, is unlikely to be the last that May and her team will have to face.