Len McCluskey, chief of the UK’s biggest trade union Unite, said he was ready to break the law by calling a strike to force further wage increases.
The Prime Minister took aim at Mr McCulskey and also Jeremy Corbyn for refusing to criticise the industrial action.
Speaking in the Commons, May said: “On the Conservative benches, we condemn illegal strikes.
“We condemn action outside the law.
“The people who suffer from illegal strikes are the ordinary working families who cannot get their children to school, who cannot access the public services they need and who cannot get to work.”
Mr McCulskey compared himself to Mahatma Gandhi and Nelson Mandela as he threatened strike action even if ballots fail to meet a 50 per cent minimum turnout.
Labour pledged in their 2017 manifesto to scrap the Trade Union Act, which makes such strikes illegal.
Appearing on the BBC Radio 4 Today Programme on Tuesday, Shadow Justice Secretary Richard Burgon refused four times to say whether he would back illegal strike action.
He said: “It’s for the trade unions to decide what actions they take.”
The threat of illegal strike action comes the Tories announced a decision to scrap the one per cent public sector pay cap.
Prison guards got a 1.7 per cent wage rise and police officers two per cent.
But Unions say these are not enough given spiralling inflation.
Speaking in the Commons, Mr Corbyn said that with inflation running at 2.9 per cent the rise in pay amounts to a pay cut in real terms.
He said: “Anything less means that dedicated public servants are worse off again and they’ve been made worse off every year for the past seven years.
“Yesterday the Prison Officers’ Association weren’t impressed either with the 1.7% offer, saying it’s a pay cut, it’s not acceptable.
“We discovered that as they are being offered, the police as well, a slightly smaller real term cut in their incomes, came the news that this would be funded by more service cuts.
“Can the Prime Minister guarantee no more police or prison officers will be lost as a result of the decisions she’s made this week?’
Mrs May replied that a lot of public sector workers have automatic pay increases over and above the one per cent because of annual increments called “progression pay” for time served in schools, the NHS, prisons and the police.
She continued: “A calculation suggests that a new police officer in 2010, thanks to progression pay and annual basic salary increases and the increase in the personal allowance that is a tax cut for people, has actually seen an increase in their pay of over £9,000 since 2010 – a real-terms increase of 32 per cent.”