Boris Johnson and Priti Patel are facing intense pressure to tighten the law on stalking as peers look set to back a new plan to force serial offenders to be registered and monitored like serious sex criminals.

An amendment to the Domestic Abuse Bill will on Monday propose a new statutory duty to monitor and manage tougher protections for victims of domestic violence and stalking.

It will also require ministers to come up with a “comprehensive perpetrator strategy”.

The cross-party amendment, tabled by Labour’s Jan Royall, is expected to win support next week, not least from several Tory peers, forcing the government to either accept it or come up with an alternative plan.

Writing for HuffPost UK, Baroness Royall said that “stalking is murder in slow motion” and it was time to create a more coherent national approach that allowed police forces across the land to better share information.

The move comes amid widespread shock and anger at the disappearance of Sarah Everard, with many MPs sharing their own personal experience of the threat of violence and harassment on the street.

Under Royall’s amendment, serial stalkers would be put on the violent and sex offender register (Visor) and subjected to monitoring and management through multi-agency public protection arrangements (Mappa) devised by police, councils and others.

The Visor database records all those required to register with the police under the Sexual Offences Act 2003, as well as those jailed for more than 12 months for violent offences and those believed to be at risk of offending.

The amendment would also require the government to provide a comprehensive perpetrator strategy for domestic abusers and stalkers within one year of the Act being passed.

The changes are intended to prevent future cases like that of Holly Gazzard, who was stalked and murdered by Asher Maslin — who was involved in 24 previous violent offences on several partners.

MPs including women and equalities chair Caroline Nokes and home affairs committee chair Yvette Cooper support the plan, and the Lords are expected to pass the amendment to force ministers to act.

Royall said that changes already made to the government’s Domestic Abuse Bill would have “a huge impact on the lives of women and children “but there is more to be done to tackle gender-based violence and misogyny”.

“Stalking is murder in slow motion, and we must treat it as seriously as other crimes. No woman should have to live in fear of their life.

“That is why I have tabled an amendment to proactively identify, assess and manage serial and repeat high-risk and high-harm domestic abusers and stalkers. Formally backed by a cross-party alliance of other peers, it would also ensure a more co-ordinated approach to data collection on perpetrators.

“A failure to properly focus on perpetrators – the men who have caused the terror and violence – will mean that many women and children will continue to be unprotected and remain at risk. That is why the government must go the extra mile and make this landmark legislation properly fit for purpose.”

Royall said that some pockets of good practice already exist, including a new pilot scheme in Sussex set up to identify and target specific stalkers for psychological therapy.

But she said adding offenders to a register “should be a matter of national policy, laid down in statute so that women are protected wherever they live, rather than the rather random locally-driven set up that we have now”.

“Perpetrators travel but information about them remains static. It is widely recognised that the current system is not working..the state has the prime responsibility for the protection of its citizens and this needs a degree of consistency across the board, as well as systems for ready exchange of data.”

Royall has a long record on the issue, with a previous amendment in 2016 accepted by ministers to double the jail sentence for stalking from five years to 10 years.

Another cross-party amendment to the Domestic Abuse Bill, tabled by Baroness Kennedy for a vote next week, seeks to make misogyny a hate crime.

It would require all police forces in England and Wales to record where existing crimes have been motivated by hatred of someone’s sex or gender.

Labour MP Stella Creasy said: “Recognising hostility towards women drives criminal offences helps us detect and prevent offences including street harassment, sexual assault, rape and domestic abuse.

“We know it works as seven police forces across the country are already taking this approach, with proven results in increasing confidence in the police and tackling violence against women.

“This is our moment for change – rather than asking women to pick a side of their identity to be protected, it is time to send a message that women should be equally able to live free from fear of assault or harm targets at them simply for who they are.”

The Home Office said that there was a strong existing framework in current legislation to tackle stalking, including new Stalking Protection Orders (SPOs), a civil order to protect victims at the earliest possible opportunity.

Home Office minister Baroness Williams of Trafford said: “Stalking is an insidious crime and the impact on its victims cannot be understated

“Under the Criminal Justice Act, individuals convicted of stalking involving fear of violence or serious alarm or distress and sentenced to a year or more are automatically subject to supervision under multi-agency protection arrangements (MAPPA).

“The Government will work with police to ensure they know how to use MAPPA to its full potential – we have also introduced Stalking Protection Orders to help police crack down on this distressing crime and have doubled maximum sentences for stalking and harassment to 10 years.”

The Home Office also part-funds the National Stalking Helpline and has allocated £211,000 to stalking-focused charities to help them to deal with the consequences of the pandemic.