INTENSE pressure is mounting on Julian Smith, the Tory Chief Whip, and Brandon Lewis, the Conservative Chairman, to quit over a bitter row in which they are accused of using “appalling conduct” to win a key Commons vote on Brexit.

The Liberal Democrats accused the senior Tories of “despicable” behaviour while Labour claimed the saga showed Theresa May’s Government was “rotten to its core”.

Even Conservatives were privately admitting the position of their two colleagues was untenable.

Yet the Prime Minister continued to stand by them, insisting the breaking of the convention - whereby MPs from opposing parties are “paired” so they cancel each other out in votes - had simply been an error.

During a visit to Northern Ireland, she told reporters: "An honest mistake was made here and both the Chief Whip and Brandon Lewis have apologised to Jo Swinson, the member for East Dunbartonshire about that."

The convention was broken earlier this week on the rebel Tory vote to keep Britain in a customs union with the EU, which the Government successfully defeated by just six votes.

Yet despite her party leader's line, reinforced by No 10 and Tory HQ, Conservative backbencher Heidi Allen revealed when she spoke to Scots-born Mr Smith about the allegations, he had been "unable to confirm to me that he did not give instructions to break pairs".

The Cambridgeshire MP said she, therefore, could "only conclude MPs were told to break pairs on Tuesday".

Ms Allen added: "I refuse to be tarnished by this behaviour so will not stand by and say nothing. Integrity and honesty are fundamental to our democracy. Anything less is unacceptable."

A former Tory Cabinet Minister was equally incensed, saying Mr Smith and Mr Lewis had “lied and abused their positions" to save their Government jobs.

"They have brought into question the integrity of Parliament and this Government through such appalling conduct. They should resign,” he added.

In the Commons, the SNP’s Pete Wishart demanded a full parliamentary inquiry into “what exactly happened”.

It was claimed as many as five Conservative MPs were “ordered” by Mr Smith to break their pairing arrangements with opposition members on the key customs union vote but only Mr Lewis did so; the others refused.

One of the Tory MPs who was paired explained: “Julian told me I was needed and told me to come in and vote. Of course, he knew I was paired. I didn’t vote and honoured my pair and he demanded to know why not afterwards. It then appears Julian told the Prime Minister it was all an innocent mistake.”

The irate backbencher added: “What happened was unacceptable. We cannot behave like this.”

Ian Lavery, the Labour Chairman, was indignant. "The Tories' story is changing by the minute as they desperately scramble to cover up their appalling actions.

"This Government is rotten to its core. Julian Smith and Brandon Lewis must now resign or be sacked and Theresa May must apologise for misleading the House," he said.

Ms Swinson, the Liberal Democrat deputy leader who had been paired with Mr Lewis for Tuesday’s vote because she was on maternity leave, tweeted: "This reflects pretty badly on those peddling the 'honest mistake' nonsense. To be fair, hats off to the two MPs who told their Chief Whip to take a running jump when he asked them to break a pairing just because the govt might lose."

As the furore unfolded at Westminster, Mrs May went to the border town of Belleek in Northern Ireland to reinforce her pledge that, post-Brexit, there would be no hard border with the Republic.

Today in a speech in Belfast, she will insist her Government has a “duty to ensure that the outcome we achieve works for the whole UK”.

The PM will stress: “For all of us who care about our country…[and] want this Union of nations to thrive, that duty goes to the heart of what it means to be a United Kingdom and what it means to be a government.

“Our job is not to deal with Brexit in theory but to make a success of it in practice for all of our people.”

Extolling the virtues of her Chequers Plan, Mrs May will urge the EU to “evolve its position” and not fall back on unworkable proposals.

Her words came after Dominic Raab, the new Brexit Secretary, met Michel Barnier, the EU’s chief negotiator, for the first time, insisting he was looking forward to “heating up the negotiations” and after their Cabinet colleague, Andrea Leadsom warned Brussels how the Chequers Plan was Britain’s “final offer” and that if it did not accept it, then there would be no deal.