Home Secretary Sajid Javid is facing a call from more than 150 MPs to press ahead with a review into demonstrations outside abortion clinics.
The review was originally ordered by his predecessor Amber Rudd who said it was "completely unacceptable" that women attending abortion clinics should feel harassed or intimidated.
Following her resignation in the wake of the Windrush scandal, MPs are set to present Mr Javid with a letter urging him to continue with the review, BBC2's Newsnight reported.
The letter was organised by Rupa Huq, the Labour MP for Ealing Central and Acton in west London where the council voted to introduce the first ban on protesters demonstrating outside an abortion clinic run by Marie Stopes.
Signatories are said to include Labour leader Jeremy Corbyn, Liberal Democrat leader Sir Vince Cable, Tory former cabinet ministers Ken Clarke and John Whittingdale, and the Conservative chairwoman of the Commons Health Committee, Sarah Wollaston.
The move is said to reflect concerns that while Ms Rudd was sympathetic to demands for curbs on protests outside clinics, Mr Javid's views on the issue are less clear.
Last month, Ealing Council in West London became the first in the UK to ban anti-abortion campaigners from protesting outside a clinic.
Councillors voted unanimously to approve a “safe zone” to shield women from demonstrators at the centre run by the charity Marie Stopes.
It followed complaints that women were being harassed and intimidated by anti-abortion protesters, some brandishing large images of foetuses and shouting “murderers” as they used the centre.
Ealing’s three-year Public Spaces Protection Order bans groups congregating within 100 metres of the clinic, which carries out about 7,000 abortions a year.
Demonstrators are also prohibited from shouting, displaying posters and playing recordings about abortion in the area. Anyone who breaches the order can be arrested and charged.
Pro-choice campaigners hailed the council’s “landmark decision”, which they hope will pave the way for authorities elsewhere in the country to implement similar measures.
Press Association contributed to this report
