A Tory peer has written to the speakers of both houses of parliament calling for Boris Johnson’s top aide Dominic Cummings to be stripped of his pass for the Palace of Westminster.

Lord Hayward said it was “inappropriate” for Mr Cummings to be allowed to move freely around the building just six months after being found in contempt of parliament for refusing to give evidence to a committee of MPs investigating the Vote Leave referendum campaign, which he led.

In a letter to Lords Speaker Lord Fowler and the Commons’ John Bercow, Lord Hayward called for an urgent review of the issue of the pass and said they should consider withdrawing it until the contempt is “purged”.

Lord Hayward was among a group of peers who raised concerns about Mr Cummings’ role in sacking Treasury special adviser Sonia Khan, who was escorted from Downing Street by armed police after being accused by the Johnson aide of maintaining contacts with the office of former chancellor Philip Hammond.

Reports suggest that Ms Khan has been offered a payoff of £40,000 following her abrupt dismissal in August.

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Speaking in the House of Lords on Wednesday, Lord Hayward asked: “Is it not acutely embarrassing to this government that they have put parliament in a position whereby it is granting a pass to somebody who is deemed to be in contempt of it? I hope that any compensation to Sonia Khan comes not from the pocket of the taxpayer, but from Dominic Cummings.”

In his letter, the peer wrote: “To most people I am sure it would seem inappropriate to issue a pass to someone when they have been found, only a few weeks earlier, to be in contempt of our procedures. A pass which gives them rights to move freely about and use the facilities of the Palace.

“I would ask therefore that this be reviewed as a matter of urgency and, if appropriate, that the pass is withdrawn until the contempt is purged.”

Lord Hayward said he understood that the pass was authorised on the grounds that it was “normal procedure” for 10 Downing Street special advisers to hold them.

And he said: “It will probably be argued that once issued the pass should not be withdrawn unless a specific offence is committed.