The call from Navin Shah follows a Labour report into the growing number of violent attacks happening inside London homes.
Mr Shah described a sex offenders-style register for domestic abusers as a "vital step" towards tackling the problem and has put pressure on London Mayor Sadiq Khan to follow Brent council's example by making a reduction in domestic violence cases a key priority.
An August report launched by Leader of the London Assembly Labour Group, Len Duvall, recommended the new course of action.
Figures show that in the year to June 2017, there were up to 150,000 incidents of domestic abuse in London, which is an increase of 800 offences.
Of these, 5,564 were reported to have taken place in Brent.
Mr Shah, talking to getwestlondon, said: “It’s shocking and unacceptable that more than 20% of reported violent crime in London is to do with domestic violence.
“I strongly believe that prevention of re-offending has to be a top priority across London and that’s where a register like the one that exists for child abusers will make a marked difference."
The introduction of a register, as put forward in the report, would require domestic abusers to make any changes to their names and addresses known to the Metropolitan Police, this is currently not a legal requirement.
It is estimated that four in 10 survivors of domestic abuse are repeat victims and current legislation means that the onus is often on the victim of an abusive relationship to report a change of address or to check a prospective partner's individual record with police.
Mr Shah added: "Current measures to protect victims are too patchy.
“We need to send a clear message to anyone committing domestic abuse that the police have them on their radar.
"A register could provide a vital step change in the way we prevent re-offending and protect people from these devastating crimes.”
"In its borough plan for 2015-2019, Brent Council made tackling domestic violence one of its main goals and I believe a register would help towards this."
Speaking at Mayor's Question Time on August 10 when Mr Duvall raised the issue, Mr Khan replied: "Can I just thank the work that Len has done in this area?
"Can I just reassure him that we are looking at how we can use the legislation we currently have? Assembly Member Duvall referred to the 400 of the most prolific offenders and the Dauntless+ work being undertaken.
"Just to reassure Assembly Member Duvall about the use of CBOs (criminal behaviour order), he is right.
"They can be used to place restrictive measures upon offenders and he will be as pleased as I was to hear that this year a Dauntless+ offender was issued with a CBO with the condition that he must inform the local police station of the details of any address at which he lives or resides for longer than 28 consecutive days and the name of any new partner within 14 days of commencing the relationship.
"He is right to remind the police via me that actually sometimes the legislation it is there; it is using it in a new way.
"The good news is the Crown Prosecution Service (CPS) and the police are working closer together than ever before, but I take on board the comments he has made and will make sure Sophie [Linden, Deputy Mayor for Policing and Crime] and the Commissioner [of Police of the Metropolis] are well aware of them.
"We will look at how we can feed this into our strategy."
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