Labour MP Rosie Duffield has called for the party to suspend Natalie Elphicke while investigating lobbying claims.
Dover MP Ms Elphicke unexpectedly defected from the Conservatives to join Labour last week.
Now former justice secretary Sir Robert Buckland has claimed she tried to lobby him, to help move the date of her then-husband Charlie Elphicke's sexual assault case to avoid publicity.
A spokesman for Ms Elphicke said the claims were "nonsense".
Charlie Elphicke was jailed in 2020 at Southwark Crown Court for two years for sexually assaulting two women.
Ms Duffield, the Labour MP for Canterbury, said Ms Elphicke should be suspended from the party pending the outcome of an investigation.
Speaking to the BBC, she said: "I think that if the shoe was on the other foot, if she was still officially a Conservative MP, we would rightly be calling for this to be thoroughly investigated and that's what should happen in this case."
She drew a comparison with Diane Abbott's suspension for remarks about racism and added "in other serious cases, like sexual allegations, before the investigation is finished the whip is removed and people suspended temporarily".
When it was put to her that the Labour Party was not planning to investigate, she said: "I think that's hugely hypocritical and I think anybody watching would think, 'well hang on, if that was a Tory MP that's exactly what we'd be calling for from the dispatch box' and therefore that should apply when it's one of our own MPs, which apparently Natalie now is."
She added she had "no reason to believe" Sir Robert, who was justice secretary and Lord Chancellor at the time, "has any reason to make this up", calling him "a greatly respected MP".
Sir Robert told the Sunday Times, external Ms Elphicke, who is trained as a lawyer, had asked him to interfere in the case and said: "She was told in no uncertain terms that it would have been completely inappropriate to speak to the judge about the trial at all."
The BBC has confirmed Sir Robert's account with him.
Speaking on Sunday with Laura Kuenssberg, shadow Cabinet Office minister Jonathan Ashworth, defended Ms Elphicke.
He said: "She says it's nonsense - it's not her interpretation of events.
"I don't understand why the Lord Chancellor at the time did not raise this and why he's raising it now, but she says it's not her interpretation."