Her firm has been ed by more than 1,000 Tesco staff and will this week take the initial legal steps for 100 of them.
Across the United Kingdom, men earned 18.4 percent more than women in April 2017, according to the Office for National Statistics (ONS) figures.
The grocer previously said that men on average were paid 14 per cent more than women in the year through April 2016.
According to the claim, Tesco warehouse staff earn from about £8.50 an hour to more than £11, while store staff earn about £8 an hour in basic pay.
"The law says women are entitled to equal pay for doing the same job or for work of equal value".
"That's 34 years to put your house in order; that's 34 years of having the advantage of paying unequally, 34 years of you making pay decisions and making financial decisions and 34 years hiding what is in open sight".
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The lawyers said the case could eventually involve 200,000 women, making it the largest equal pay challenge in the UK.
Leigh Day said it had already started submitting claims on behalf of its clients through conciliation service ACAS, the first stage in the Employment Tribunal process.
If even a small proportion of the women are successful, the bill for Tesco would be significant.
As the United Kingdom forces companies to disclose the gap between men's and women's pay, the country's biggest private employer is confronted with a huge demand from workers feeling short-changed.
Their pay was below men in comparable jobs such as bin collectors and road workers.
However, analysts at HSBC said: 'This is not a gender pay issue.
Tesco said it was unable to comment on the claim as it had not received it.
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Tesco said they work hard to ensure all staff are paid "fairly and equally".
This comes as research has also revealed that mothers continued to be penalised at work, as they look to find part-time roles. Of Tesco's lowest paid workers 62 per cent are women, but only 41 per cent of its highest earners are female.
"We deal with customers, they [the men] don't have to".
It comes after a review by the chief executive of The Royal Society of Arts Matthew Taylor said previous year that many Britons working for firms in the gig economy deserved more entitlements.
"Although we think we have equal rights, there are times where there are discrepancies and you can't explain them", she said.
Last week EasyJet CEO Johan Lundgren agreed to a £34,000 pay cut to match the salary of his female predecessor, Carolyn McCall, in a bid to affirm the companies commitment to addressing the gender pay gap imbalance.
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