Liberal MP Alan Tudge has quit Scott Morrison's cabinet after he was accused of abusing one of his former staffers, who he was having a consensual affair with.

Mr Tudge has strenuously denied the allegation, but he stood aside as education minister late last year while the government investigated.

Late on Friday the Prime Minister said that review found Mr Tudge had not breached ministerial standards, but he said Mr Tudge had quit the frontbench in the interests of his family as he seeks re-election.

The investigation was launched when Mr Tudge's former media adviser, Rachelle Miller, went public with her claim.

The pair were involved in a consensual affair in 2017.

Ms Miller did not participate in the inquiry because she said the terms of the investigation "forbade it from investigating any allegations which might amount to criminal conduct".

Mr Tudge, in a written statement, insisted it was the second time the allegations against him had been "dismissed".

While he said he would not comment further, his statement noted that he would not seek to return to the frontbench "before the election".

"I deeply regret the consensual affair with Ms Miller in the second half of 2017 when both of us were married with children and in our forties," he said.

"It should never have happened and it has caused hurt to our respective families. It caused the end of my marriage that year."

More to come.