The former prime minister described the welfare reforms as a “cruel and vindictive” experiment that will exacerbate the “convulsions” of Brexit and risk public disorder.
His intervention comes as charities warn extending the coverage of universal credit across the country would trigger a surge in food bank usage.
Reports have suggested millions of families could be left more than £200 a month worse off when the new system begins its national roll-out in July.
Writing in the Daily Mirror, Mr Brown said universal credit would remove £3bn from the social security budget on top of cuts to child tax credits and benefit, which he helped introduce.
He warned that child poverty was rising “inexorably” and is expected to hit five million in 2022.
“It is now time to abandon the national roll-out of the disastrous benefit-cutting universal credit,” he said.
“Call a halt to this experiment - cruel and vindictive far beyond austerity - that is pushing child poverty among millions of hard-working British families to record levels.
“From next July when three million more families begin to be herded on to universal credit, our country will face the kind of chaos we have not seen since the days of the hated poll tax.
“With the convulsions of Brexit in March and the universal credit four months later we face a summer of division and despair.”
Labour had planned on pausing the scheme’s expansion if it gets into government, but Mr McDonnell said the party would now scrap it.
Touted as the most radical reform to welfare since the Second World War, universal credit combines six means-tested benefits and tax credits into one payment.
It is also designed to encourage people to take up work by ensuring they will always be better off having a job.
However, critics have warned that in areas where the system has already been introduced there has been an increase in food bank use.
Food bank charity the Trussell Trust said it had received reports people had not been able to access the help they require.
The poll tax riots in March 1990 erupted after a peaceful march by 70,000 protesters in London broke down into violent disorder, leading to 400 arrests and more than 100 injuries.
Opposition to the Community Charge, dubbed the poll tax and later revised into council tax, contributed to the downfall of Margaret Thatcher, who resigned as prime minister later that year.
Additional reporting by PA
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