Businesses with more than 100 employees must be required by law to publish their gender pay gap data, according to a group of MPs.
Businesses would also have to report pay gaps between staff from different ethnic groups and draw up plans for tackling imbalances under proposed legislation being presented in parliament on Tuesday.
Stella Creasy, who will introduce the pay transparency bill, said the government "should pull its finger out" on an issue that had become all the more pressing as the COVID-19 pandemic deepens inequalities.
The gender pay gap is the difference between the average earnings of men and women.
From 2017, any organisation with 250 or more employees had to publish specific figures about their gender pay gap on their website, and report the data to the government.
"There has never been a more important time to really get to grips with this inequality.
"Equal pay legislation was brought in before I was born and we still don't have equality. I don't want my daughter still facing the same questions," Ms Creasy said.
The Equal Pay Implementation and Claims Bill (EPIC) 2020 has cross-party backing.
Signatories for the law include Caroline Nokes from the Tory chair of the Women and Equalities Committee, the Liberal Democrats' Christine Jardine, the SNP's Anne McLaughlin and the Green Party's Caroline Lucas.
Equality experts said they were not aware of any other country that requires companies to publish ethnicity pay gaps, calling the proposal a chance for Britain to lead by example.
Figures from the Office for National Statistics (ONS) showed in the year to April 2019, the gender pay gap for full-time workers rose to 8.9%
But for people under 40, the gap for full-time employees was close to zero.
Meanwhile, ethnic minority pay gaps range from 1.4% in Wales to 23.8% in London, according to official statistics, but the figures mask big variations between different minorities.
Creasy said the difference was narrowing even more slowly than the gender pay gap.
Equality experts say a key reason why gender pay discrimination continues to be so prevalent is the lack of workplace pay transparency, and that the proposed reforms would make it easier for women to bring equal pay claims.
In the proposal, Ms Creasy and her supporters are calling for a number of new measures to be introduced alongside the rise in the threshold, including, allowing women to request pay data relating to a male colleague if they suspect there is a gap, requiring mandatory plans of action to fix any gap and ending time limits on women being able to claim back pay.
The Equal Pay Implementation and Claims Bill (EPIC) 2020 from Ms Creasy is a Ten Minute Rule Bill - a procedure that lets backbench MPs make their case for a new law in a speech lasting up to ten minutes.