Breaking House of Commons voting conventions has “appalling consequences for the management of government”, Michael Heseltine has warned, as Theresa May continued to insist this week’s breach of pairing rules was an honest mistake.

Lord Heseltine, who was a cabinet minister when John Major’s government was defeated over the Maastricht treaty, said he was deeply concerned at the idea of May pushing through Brexit legislation using “any device, threat, or chicanery”.

“There is no excuse for breaking one’s word,” he told BBC Radio 4’s The World at One. “Breaking a pair has the most appalling consequences for the management of government in this country.”

On Thursday, Conservatives sources conceded that the chief whip, Julian Smith, had asked several Tory MPs to break pairing arrangements during a hugely close Commons vote earlier in the week, but most had refused to do so.

Jo Swinson pairing row: Conservatives admit chief whip asked MPs to break arrangements Read more

The only one who did obey the instruction, the party chair, Brandon Lewis, was paired to Jo Swinson, the Liberal Democrat deputy leader, who is on maternity leave. She responded with fury, as did many other MPs.

The Conservative sources said that while Smith asked some people to break short-term pairing arrangements, in which a government MP misses a vote because an opposition member is unable to attend, he made an error in asking Lewis to vote.

Asked about the issue following a speech in Belfast on Friday, May said: “There was an honest mistake made, for which the chief whip and indeed Brandon Lewis have both apologised to the member concerned.”

Gavin Williamson, asked whether he, a former chief whip, believed Smith should resign, said: “No I don’t. I haven’t got any of the details as to what happened but what the government has been absolutely committed to doing is delivering the will of the British people which was given in terms of the referendum, and that is what this government will deliver on as we exit the European Union.”

Labour's deputy leader, Tom Watson, called the explanations for the breach “desperate and blatantly untrue”, and said Smith and Lewis should resign or be sacked. “This is about public trust in politics,” he said. "At such a crucial time for our country, people expect candour and decency, not cowardice and dishonesty.”

Heseltine, who as a young MP in 1976 grabbed the Commons mace in fury at the then Labour government’s decision to breach pairing to force through a measure by one vote, said it was a huge mistake for whips to try such a tactic.

He said the practice was needed to prevent the spectacle of ambulances arriving at parliament so seriously ill MPs could vote in close divisions, as was previously the case.

“It was a gruesome and inhuman way to treat often elderly members of the house in extreme circumstances of pain,” he said.“ So you have a pairing system. But the pairing system relies on one word – trust. My word is my bond, if you don’t vote I won’t vote. If you can’t believe that then the pairing system collapses and the business of parliament becomes chaotic.”

Heseltine said he had no view on the individual circumstances of what Smith did – “I don’t know the people, I wasn’t there, I don’t know what was said” – but called for efforts to correct any such errors: “The only way to make the place workable is to restore trust. And therefore assurances have to be given.”

He said it was particularly worrying that such tactics were being used over Brexit: “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 or chicanery that the government can turn its hand to.”

Smith was under intense pressure to see off a Tory rebel amendment on Tuesday’s trade bill, which called for the UK to remain in a customs union with the EU if a free trade deal could not be negotiated quickly. The Conservatives narrowly won by six votes.

Asked on Friday if May still had confidence in her chief whip, her spokeswoman said the PM did. She added: “We take the convention of pairing very seriously. The one incident where a pair was broken was a mistake. As the PM said in the house, it wasn’t good enough, and can’t be repeated.”

Lewis voted only twice in the trade bill debate. One was on a vote on staying in the customs union if the UK fails to agree a trade deal with the EU, which was narrowly defeated by the government by 307 to 301. Lewis also voted on the amendment relating to EU medicines regulation, which the government lost by four, 305 to 301.