MPs have called for parliament to consider whether Andrew Mountbatten-Windsor should lose his potential right to inherit the throne in the after his arrest.

Andrew was arrested and questioned by detectives on Thursday on suspicion of misconduct in public office, in connection with allegations that the former prince shared confidential material with Jeffrey Epstein.

Andrew remains eighth in line to the throne after Princes William and Harry and their children, despite him having relinquished his royal titles in October after new information came to light about his links to Epstein, the late financier and child sex offender.

This means Andrew is still a counsellor of state, the group of adult royals who could be named to fill in for King Charles if he was ill or abroad, even if in practice this would never happen for him, as only working royals are used.

The Liberal Democrats called on Friday for the issue to be considered. “The most important thing right now is that the police be allowed to get on with their job, acting without fear or favour,” Ed Davey, the Lib Dem leader, said in a statement.

“But clearly this is an issue that parliament is going to have to consider when the time is right, naturally the Monarchy will want to make sure he can never become king.”

Andrew Bowie, the Conservatives’ shadow Scotland secretary, made a similar argument, telling GB News it would be “the decent thing” for Andrew to be removed.

Bowie said: “Of course, if he’s found guilty of this, I think parliament would be well within its rights to act to remove him from the line of succession.

“But, let’s remember, he’s not been found guilty of anything just yet – he has yet to be charged with anything. So we have to let the police investigation run its course, and I think we should all act accordingly subsequent to that.”

Among Labour MPs, Rachael Maskell, who represents York Central, said it seemed likely that parliament would need to act.

“From the evidence already held in the public domain, it is clear that his position as a counsellor of state and with succession rights are removed, as well as all titles,” she said.

“I trust that legislation can be passed to achieve this. I am glad that the king seeks to be as helpful as he can, and providing support to parliament to act would assist in this.”

The SNP’s Westminster leader, Stephen Flynn, has also called for action to be taken to remove any risk of Andrew becoming head of state, while the Labour MP Richard Burgon, called for an independent inquiry into what the wider royal family knew about Andrew’s links to Epstein, adding: “It’s time for a serious national debate about abolishing the monarchy.”

Zack Polanski, leader of the Green party in England and Wales, which supports the abolition of the monarchy, said he believed Andrew’s case could hasten this moment.

“When the public are ready to have that national conversation about the monarchy, I think issues like this certainly don’t help the monarchy’s case,” he told reporters while campaigning for next week’s Gorton and Denton byelection.