Over a hundred employers have signed the pledge as part of a campaign led by Fawcett East London, a grassroots arm of gender equality charity the Fawcett Society.
More than 30 US states have banned salary history questions, preventing employers from asking prospective employees about their current or previous salaries during job interviews or on application forms.
Naomi Elster, who leads the Fawcett East London campaign, said a similar law in the UK could reduce pay gaps and stop past discrimination in pay being carried forward.
Speaking to HR magazine, she said: “The evidence is really clear that removing salary history is a really simple and effective way to start closing the gender pay gap.
“The simplest way to think about why this might be that you only need to be underpaid once for it to potentially follow you for your entire career, and there are lots of reasons that women can end up being underpaid.
“Salary history bans are easy for employers to introduce – all it takes is a tweak to application forms – but they have a big impact, not just on the pay gap but also on team dynamics.”
Research from the Fawcett Society found 90% of people feel salary history is an unfair way for pay to be decided.
Jemima Olchawski, Fawcett Society chief executive, said salaries should be decided based on skills and experience.
She added: “Employers ought to decide what salary to pay someone based on the skills and experience required for each role, not what a person previously earned. Closing the gender pay gap is vital for tackling other economic disparities between men and women, such as the gap in retirement savings.”