A Conservative former minister arrested on suspicion of rape must not be named by MPs, the Commons Speaker has urged.

Sir Lindsay Hoyle claimed such a move would be “wholly inappropriate” while police investigate, and asked for MPs to cooperate with his advice.

Parliamentary privilege grants certain legal immunities for MPs and peers when speaking in the Commons and Lords, and has been used previously to identify people subject to legal proceedings and misconduct allegations.

Sir Lindsay also confirmed the Conservative MP has “voluntarily agreed” not to attend the House of Commons for the period of his bail.

Prime Minister Boris Johnson has been criticised for not suspending the MP from the Conservative Party, insisting a decision will be made when the police investigation is concluded.

The Metropolitan Police received allegations on July 31 of sexual offences and assault relating to four incidents at addresses in London, including in Westminster.

The force said a man was arrested on August 1 on suspicion of rape and taken into custody at an east London police station.

He was released on bail until November.

Sir Lindsay, in a statement to the Commons, said: “The House will know that a member has been arrested in connection with an investigation into an allegation of a very serious criminal offence.

“I have received assurances from the member and the Government Chief Whip that the member has voluntarily agreed not to attend the House of Commons for the period of the bail.

“I, the House of Commons Commission and the House service take the safety of our staff and the parliamentary community as a whole very seriously, and ensuring any necessary measures are taken in respect of MPs and employers and staff.”

He added: “While the investigation is ongoing, I believe it would be wholly inappropriate for any further reference to be made to this matter in the House, including any attempt to name the member concerned.

“I would appreciate your co-operation on this matter.”

Garry Graham, Prospect deputy general secretary, said in a statement: “The agreement that the MP shouldn’t come into Westminster, reached with the MP himself, is no replacement for a proper policy.

“Parliamentary unions agree that the House of Commons needs to set an example in this.”