Anti-austerity campaigners marched from Clerkenwell Green to Trafalgar Square in the annual bank holiday protest to mark International Workers’ Day.
Speaking to journalists after addressing demonstrators, Mr McDonnell attacked Mrs May for being "clueless" and unprepared for talks at Number 10 with European Commission president Jean Claude Juncker last Wednesday, as it was reported their discussion went badly.
He said: "What I find came out of it is that she apparently appeared clueless.
"I find it deeply worrying. She either went in badly briefed or she just couldn't handle the situation.
"We're finding that just as she refused to debate with Jeremy, this concept of a 'strong and stable' leader, she's demonstrating that actually, she's not strong, she's wrong.
"As for stable, pretty feeble."
Comparing the two main party leaders, the shadow chancellor repeatedly criticised the Prime Minister's refusal to take part in TV debates, saying it demonstrates two types of leader.
He said of the Prime Minister: "One is a leader who is trying to act in a traditional way...spin, slogans that you repeat ad nauseum.
"Or a leader that's a warm human being who shows true leadership that brings people together, building consensus, having policies and putting them out. That's the sort of leader I want", he said of Jeremy Corbyn.
A staunch Corbyn ally, he laughed off questions about former Labour leader Tony Blair's return to politics announced on Sunday, but Mr McDonnell welcomed the contributions of Labour 20 years ago, as "building the foundations".
Listing off Labour policies under Mr Blair including the introduction on the National Minimum Wage, he said: "You build upon the foundations of that era. I was elected in '97 and we did some fantastic things.
"What we're advocating now is building on what Labour did in power in that period and then moving it on to address the issues we're now facing."
Mr McDonnell also renewed Labour's pledge for new employment rights, as it was announced over the weekend that a 20-point plan under Labour to end a "rigged economy" would include securing a £10 minimum wage, end zero-hours contracts and ensure equal tights for pregnant women in the workplace.
He said: "This is a government that after seven years, we're the only developing country where growth is returning but wages are stagnating.
"That's why we need a new charter for workers' rights in this country.
To cheers from protesters, who represented trade unions in Britain and internationally, Mr McDonnell said: "Let me tell you what we will do in June, when June becomes the end of May."
He also insisted on a 1:20 pay ratio - meaning public sector and private firm bosses performing government work are not paid more than 20 times the wage of the firm's lowest paid employee - for all firms competing for a government contract.
Mr McDonnell also pledged to scrap the Trade Union Act.
Labour leader Jeremy Corbyn, who was on the campaign trail and did not attend, sent a message read out to May Day protesters by Mr McDonnell.
He said: "May Day greetings for peace around the world.
"Workers together want rights to organise and be represented.
"The policies we've announced on workers' rights this week all have their origins in working class organisations and demands.
"United, we can win."
This year's May Day march to celebrate the contribution of workers wound down with a Trafalgar Square rally after making its way through central London.