Sir Lindsay Hoyle said it is “extremely concerning” that Wayne Couzens was deployed to the Houses of Parliament as an armed officer, adding it raises questions about police vetting procedures.
It comes as a former senior Met Police officer called for all officers to be re-vetted as an “urgent” measure to reassure the public.
Couzens was handed a whole life sentence at the Old Bailey on Thursday by Lord Justice Fulford, who said his “warped, selfish and brutal” offences had eroded confidence in the police.
Ms Everard, 33, was walking home from a friend’s house in Clapham, south London, on the evening of March 3 when she was kidnapped, raped and murdered by Couzens, 48.
The Met Police had previously said Couzens moved to the Parliamentary and Diplomatic Protection Command in February 2020 where his primary role was to patrol diplomatic premises, mainly embassies.
On Saturday, a Met spokesman said: “Couzens was deployed to armed static protection duties on the Parliamentary Estate on five occasions from February to July 2020.”
The Parliamentary Estate includes the Palace of Westminster – the location of the House of Commons and House of Lords.
Sir Lindsay said: “Like everyone, I have been sickened by the depravity of Wayne Couzens – and heartbroken for the family of Sarah Everard.
“The news that Couzens was deployed as an armed officer on the Parliamentary Estate is extremely concerning and raises a number of questions about police vetting procedures.
“To that end, I have asked the Met Police to meet me urgently to discuss how this person could have been deemed suitable for deployment here.
“Further, I will be seeking reassurance that at no time was anyone on the Parliamentary Estate put at risk.
“The security of members and staff has always been my number one priority, so I want to know how this man could ever have crossed the parliamentary threshold.”
Couzens was said in court to have been “attracted to brutal sexual pornography” as far back as 2002.
The police watchdog previously said he was linked to a flashing incident in 2015, and two more incidents just days before he killed Ms Everard.
Parm Sandhu, an ex-chief superintendent at the Met, said urgent action is needed to restore public confidence in the police.
She told Sky News’s Trevor Phillips on Sunday: “Everybody who works in policing now should be re-vetted. Those people who got through the vetting procedure 20 years ago, 30 years ago, all of them.
“Every single person needs to be reviewed and if anything comes up in their past – it doesn’t have to be a conviction, it just needs to be come to notice, because this man did come to notice.
“So every person should be re-vetted and reassessed as to whether or not they are safe to be working with members of the community and members of the public.
“It needs to be done now as an urgent measure to reassure the public and rebuild the trust and confidence that policing has lost, but it needs to be done on a regular basis so that we don’t have anybody that even comes close to the actions of Wayne Couzens.”
Meanwhile, Police Scotland said they are introducing a new verification check that lone officers will offer members of the public they speak to, in response to Couzens using his warrant card to falsely arrest Ms Everard before her murder.
From Saturday, the force said officers operating on their own will proactively offer to carry out a verification check for anyone they come across who appears to be concerned for their safety.
This will involve the officer’s radio being put on loudspeaker and a member of the control room staff confirming who they are.
Police Scotland said its constables normally operate in pairs but there may be rare cases when a lone officer approaches a member of the public.