In a speech in Edinburgh, Mr Brown said he feared a repeat of the violent anti-poll tax riots in 1990 that helped drive Margaret Thatcher out of office, unless Mrs May’s government cancelled next year’s national roll-out of Universal Credit.
The system is being trialled gradually across the country to replace six separate welfare payments and is designed to be simpler and ensure people are always be better off in work than out.
But the project is beset by claims it has been botched, leaving claimants in hardship waiting for delayed payments.
Ministers are said to have been warned it could also leave many people £200-a-month worse off though the Government says there is a package in place to stop claimants losing money
Charities say its nationwide introduction next year will trigger a surge in people relying on food banks.
Mr Brown said UC would take a further £3billion out of the welfare budget and the number of children in poverty was on course to hit five million by 2022.
“A return to poll tax-style chaos in a summer of discontent lies ahead,” he added.
A Downing Street source said: “I’m not sure that the Prime Minister is going to take any lessons from Gordon Brown on this particular issue.
“Under his system of tax credits, not only did some people have unclaimed benefits because the system was too complicated, you also had a situation where MPs were recipients of benefits.
“It was clearly a system that doesn’t work and we think Universal Credit is better.”
Earlier at Commons Question Time, Mrs May hit back at Jeremy Corbyn’s accusations over benefit cuts.
She told him: “What we see in the changes that we are putting forward in relation to welfare reform is encouraging people into work and making sure that when they get into work, work pays.
“I might also say to you that there are £2.4billion of unclaimed benefits under the legacy system of the Labour party that will be paid to people under UC – 700,000 people getting the benefits that they are entitled to under UC for the future.”
Labour now says it will scrap UC.
But a senior source also stressed: “We don’t support riots.”