Relocating MPs and peers to York against their will during major renovations of the Palace of Westminster is “highly unlikely”, according to a Cabinet minister.

Commons Leader Jacob Rees-Mogg was pressed to guarantee that Westminster will remain the home of Parliament after Boris Johnson floated York as a temporary home.

In a letter, the Prime Minister said that locations outside London should be considered as a review is under way on how to handle the repair works at Parliament, which some estimates state could cost £6 billion.

Conservative Sir Bernard Jenkin, chairman of the Liaison Committee, questioned the suggestion and told the Commons: “I’ve listened carefully to what (Mr Rees-Mogg) has been saying. He’s laid great emphasis on saving the building, the Palace of Westminster.

“But can he just clarify it is the policy of the Government that this should be saved in order that it should be the home of our national Parliament, permanently?”

Mr Rees-Mogg replied: “I think (Sir Bernard) may be alluding to the mention in the Prime Minister’s letter of York and I would remind (Sir Bernard) that between 1301 and 1335, Parliament met in York 11 times, but that when Edward IV tried to get it to move to York it was unsuccessful.

“And so it will end being a matter for parliamentarians as to where this House sits.

“Though strictly speaking, the meeting of Parliament is called by the sovereign to her palace at Westminster and that, I think, is something that it would be highly unlikely to change without the acceptance of parliamentarians.”

Sir Bernard later said: “It may be so obvious as to be implied, but it would be a good thing if it was just explicitly the policy of the Government that the Government envisages staying permanently in this building, even if we decant for a period, even if the House of Commons chooses to meet in different parts of the country at different times, that this remains our national home.”

Meg Hillier, Labour chairwoman of the Public Accounts Committee, cautioned MPs to be aware of the “smoke and mirrors” from Downing Street.

She said: “I put the move to York for the House of Lords in the same category as the bridge to Northern Ireland or the estuary airport or the garden bridge.”

The PM has said costs for Parliament’s renovation should be “kept to a minimum”, something Mr Rees-Mogg echoed in a debate on the project.

He warned the work is not an opportunity to “create a second Versailles” and there can be “no blank cheque”.

Mr Rees-Mogg went on: “Our goal should be a narrow, simple one – to save the Palace of Westminster without spending more than is necessary. That is the only way we’ll be able to look our constituents in the eye as we explain the steps being taken.”