THERESA May’s attempt to draw a line under the Westminster votes row failed after Labour upped the ante, accusing the Tories of “cowardice and dishonesty”.

The Prime Minister, taking questions from reporters in Belfast, was asked again about the alleged duplicity of her Chief Whip Julian Smith in the row over the breaking of “pairing” arrangements in the Commons earlier this week.

Mrs May once more insisted it had been an “honest mistake” and that Mr Smith had apologised to Jo Swinson, the deputy Liberal Democrat leader, who had paired with Brandon Lewis, the Tory Chairman, on the key customs union vote on Tuesday; a vote the Government narrowly won by six votes.

Pairing is a convention whereby MPs from opposing parties agree to absent themselves and so cancel out each other’s vote. Ms Swinson, the MP for East Dunbartonshire, is currently on maternity leave.

While Mrs May repeated the Conservatives’ official line, it has transpired that Scots-born Mr Smith “ordered” as many as five Tory MPs to break their pairing arrangements in the key customs union vote; only Mr Lewis did so.

One senior Tory source noted: “We can’t say no instructions were given about breaking short-term pairing arrangements, we can’t say that we didn’t think about it. This does happen; so far in this parliament 66 pairs have been broken, 52 by opposition parties.”

But Labour refused to let the matter lie and stepped up its calls for the PM to sack Mr Smith and Mr Lewis if they failed to resign.

Tom Watson, the party’s deputy leader, said: "It is unbelievable that the Prime Minister has repeated the desperate and blatantly untrue excuses made by her party Chair and Chief Whip.

"This is a serious issue that goes beyond efficient administration in the House of Commons. This is about public trust in politics. At such a crucial time for our country, people expect candour and decency, not cowardice and dishonesty.”

The Midlands MP went on: "Theresa May was right to call the Tories the 'nasty party' and nothing has changed.

"From forcing seriously ill MPs into the Commons in their wheelchairs, carrying sick buckets, to cheating a new mum out of her vote, this Government is rotten to its core.

"If Brandon Lewis and Julian Smith, two generals of the nasty party, don't have the honour to resign, the Prime Minister should find the strength to sack them," he added.

Tory grandee Lord Heseltine intervened to insist there was “no excuse for breaking one's word”.

The pro-EU former Deputy Prime Minister said: "It is to me unthinkable that the biggest peacetime political disaster of my life is being forced through the House of Commons with any device, threat, chicanery that the Government can turn its hands to."

Earlier this week, Andrea Leadsom, the Commons Leader, said there would be a debate on proxy voting, which would end the need for pairing, in September.