The lawyers acting for the 170 women who brought the original case against Birmingham City Council say this marks "an historic decision".
"This is a great day for equality and for all those women massively underpaid over many years within public and private organisations.
"Birmingham Council should now do the decent thing and settle the claims. They saved money by underpaying ex-workers for so many years, and so should now stop wasting taxpayers’ money fighting court cases they cannot win."
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Ms Leadsom has received the backing of Ian Duncan Smith, the former work and pensions secretary.
"This was mindless vandalism at its very worst, which has wrecked a much-loved community facility."
Three people have been taken to hospital after a taxi collided with pedestrians and a lamppost this afternoon.