Asda is facing mass legal action from thousands of female employees who claim they are paid less than men to do equally valuable jobs at the supermarket chain.

Law firm Leigh Day said that since revealing in April it was representing 400 Asda employees it had been approached by more than 19,000.

The mostly female Asda shopfloor staff claim they are underpaid compared with mostly male colleagues working in the supermarket’s warehouses.

The case could become the largest ever employment claim in the private sector, the lawyers said. If Asda, which employs 170,000 staff working across 370 stores and 23 depots, loses the claim it could be forced to pay staff the difference in earnings going back six years.

Michael Newman, a discrimination and employment law expert at Leigh Day, said: “In the supermarkets the checkout staff and shelf-stackers are mostly women. The people in the warehouses are pretty much all men. And, as a whole, the group that is mostly men gets paid more.

“Our investigations suggest that the jobs are pretty much the same, in that warehouse staff are responsible for taking items off shelves, putting them on pallets and loading them into lorries. In the supermarket, they do the reverse: taking the pallets off the lorries, unstacking them and putting the items on the shelves. Where the jobs are not similar, we still think they are of equal value.”

A spokesperson for Asda said: “A firm of no-win, no-fee lawyers are hoping to challenge our award-winning reputation as an equal opportunities employer. We do not discriminate and are very proud of our record in this area which, if it comes to it, we will robustly defend.”

If the legal action succeeds other supermarkets who also own their distribution centres may face similar claims. Most retailers own some of their distribution centres and lease others and use a mix of directly employed and third-party staff.

Morrisons directly employs nearly three-quarters of staff in its distribution network. Tesco said it directly employs the majority of such staff even though it leases most of its distribution centres.

Sainsbury’s refused to comment on the employment status of its distribution staff but said it owned most of the facilities they work in. John Lewis directly employs 3,500 staff in its distribution network, the vast majority of such workers, while Marks & Spencer employs just a fifth of its staff directly.

Unequal pay has been a big battleground in the public sector, with female cleaners and dinner ladies taking legal action over claims they were paid less than men who worked as binmen or street cleaners.

Birmingham city council has agreed to pay more than £1bn to settle the claims of tens of thousands of women which go back over many years.