The letter was organised by Rupa Huq, the Labour MP for Ealing Central and Acton in west London where the council voted to introduce a censorship zone which criminalises prayer and support outside a Marie Stopes clinic.
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.
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.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.
