Liberal MP Alan Tudge has quit the federal cabinet. 

Mr Tudge has moved to the backbench following an investigation launched after his former media adviser, Rachelle Miller, went public with claims of emotional and physical abuse suffered during a consensual affair the two were involved in. 

The investigation by intelligence specialist Dr Vivienne Thom into the allegations found no evidence to suggest the former minister breached the code of conduct that was in place at the time. 

Dr Thom conceded that the former staffer's decision not to participate limited the evidence available to the inquiry.

Ms Miller says she did not participate in the inquiry because the terms of the investigation “forbade it from investigating any allegations which might amount to criminal conduct”. She said the terms of reference and time frame guaranteed a narrative that suited the government's agenda.

Dr Thom also said that “the Ministerial Standards do not specifically address broader integrity and conflict of interest issues that can be a consequence of relationships that do not amount to ongoing or family relationships”. 

A change was made to the Ministerial Standards in 2018 by then-prime minister Malcolm Turnbull, known as the “bonk ban”, after the alleged events aired by Ms Miller occurred. 

“I conclude from Mr Turnbull's comments about the amendment that a Minister engaging in sexual relations with staff would not have been considered to have breached the 2015 Standards,” Dr Thom said.

“For this reason, Mr Tudge's intimate relationship with Ms Miller was not, in itself, a breach of the 2015 Standards.”

Mr Tudge has strenuously denied Ms Miller's allegations, while alleged screenshots of conversations between the two in early 2018 reveal he was at least highly paranoid over what was at stake if the affair was made public.

“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.”

Mr Tudge had been on leave since the investigation started in November last year. 

Prime Minister Scott Morrison says Mr Tudge had dropped his frontbench roles “in order to  focus on his re-election as the Member for Aston”. 

Mr Tudge has held the safe Liberal electorate of Aston, in Melbourne's outer eastern suburbs, since 2010.