Senior Tories have come under fresh pressure after claims that they deliberately broke voting pacts during a knife-edge Brexit vote.
Chief Whip Julian Smith apologised and said Tory Party chairman Brandon Lewis had been “asked to vote in error” after a pairing agreement with a senior opposition MP on maternity leave was broken.
Mr Lewis said it had been an “honest mistake” in fast-moving circumstances.
But the party chairman and two other Tory MPs were told by Mr Smith that they should go ahead and vote despite being paired, according to the Times.
It said the two unnamed MPs both sought further advice and ignored the instruction.
The Conservative Party did not deny the allegations.
Labour has demanded the resignations of the two senior Tories if they fail to give a full explanation over the whipping operation.
Mr Lewis had been “paired” with Liberal Democrat deputy leader Jo Swinson, meaning neither would walk through the voting lobbies.
But the Tory MP then took part in two crunch Commons votes on Tuesday night and helped Theresa May narrowly avoid a damaging defeat on Brexit trade plans.
During Prime Minister’s questions, Mrs May told MPs: “The breaking of the pair was done in error. It wasn’t good enough and will not be repeated.”
Labour said the Chief Whip and the party chairman should quit if they could not account for what happened.
Conservative MP Heidi Allen also raised concerns about the claims.
She said: “I sincerely hope this isn’t true. No matter how tough the going gets, principle, integrity and standards matter. Without those, what’s left?”
Shadow equalities secretary Dawn Butler said: “If these reports are correct, the Tory whips, Brandon Lewis and even the Prime Minister have been telling untruths about their shocking move against an MP on maternity leave.
“Breaking a pairing arrangement was a desperate move by a collapsing Government and makes politics even more inaccessible for women.
“We need a full, honest explanation of what’s gone on. If they can’t do so, surely the Chief Whip and Conservative Party chair should resign.”
The actions did not change the result of the votes but the Government only narrowly scraped through.
Downing Street said Mrs May still had full confidence in Mr Smith.
Asked if the PM stood by her comments that the pact had been broken in error, a spokeswoman replied: “Yes, absolutely.”
The Liberal Democrats called for the Chief Whip to make a statement to the House.
A spokesman said: “The Conservatives have clearly broken the pairing convention and possibly misled Parliament in calling the vote ‘a mistake’.”
SNP Westminster leader Pete Wishart asked in the Commons for a full inquiry into the breakdown of pairing.
Conservative Peter Bone (Wellingborough) said he was “very concerned” to hear that a pairing was broken.
Commons Leader Andrea Leadsom said: “A pair was broken, people were extremely apologetic, it was an error.”
On Wednesday Ms Leadsom told MPs Mr Lewis was “absolutely blameless” in the matter.
A Conservative spokesman said: “We have apologised for the fact that a pregnancy pairing arrangement was broken in error this week.
“No other pairs offered on the Trade Bill on Tuesday were broken.”
Lib Dem chief whip Alistair Carmichael, who secured an urgent question on the matter on Wednesday, later told MPs that after meeting Mr Smith he still did not understand how the error had occurred.
Mr Carmichael, speaking at business questions, said: “I have somewhat of a novel request for the Leader of the House and that is that the Government Chief Whip should come to the despatch box and make a statement himself.
“Now I’ve been here long enough to know the conventions, I know the convention is that the Government Chief Whip does not speak in the House, but conventions are exactly that, ours is a system of checks and balances, if you take out a check then you have to adjust a balance.”
Ms Leadsom did not respond directly to the request but again apologised for the “error”.