Mr McDonnell hit out at Mr Hammond for the comments he allegedly made at a Cabinet meeting last week on the Andrew Marr show yesterday, saying he had been on the picket line with striking hospitals cleaners in London the day before and one worker had given him her payslip.
"But when you take into account the very generous contributions that public sector employers have to pay in for their workers' pensions, their very generous pensions, they are still about 10 per cent ahead". First secretary Damian Green said: 'Now is absolutely not the time for this type of activity'.
And a separate report said that he had told colleagues that public sector workers were overpaid compared to those in the private sector.
As Mr Hammond continued speaking, Ms May reportedly said: "Chancellor I am going to take your shovel away from you" - a reference to the adage: "When you're in a hole, stop digging".
Former party leader Ian Duncan Smith told the BBC there was no appetite among conservative lawmakers for a leadership contest and said his colleagues should "shut up" and "let everyone else get on with the business of governing".
He was pointing out that public sector earnings are still higher than those in the private sector, despite years of pay restraint after the credit crunch sent the economy into a tailspin.
"Our backbenchers are furious and the only people smiling at this will be in Berlin and Paris", declared the Scot.
Damian Green appeared on BBC Radio 5Live's Pienaar's Politics in an attempt to calm the down the rows between various factions. "What I would say is that the Government is all working together to deliver Brexit, which delivers on the will of the British people".
But The Sunday Times quotes a Cabinet source saying: Philip used a fairly inflammatory phrase.
JP: "Put the record straight for us then".
The comments are likely to spark a backlash with public sector workers, who have been campaigning for the current 1% pay cap to be lifted.
But the Chancellor does not think that public sector workers are overpaid the Government obviously respects the millions of people who do really important jobs. After seven years of a punishing pay cap, all public sector employees need a pay rise. He accused those leaking as having "too much self-indulgence".
He made the comments amid the news that Chancellor Philip Hammond has come under fire after it was claimed that the he told Cabinet colleagues that public sector workers are "overpaid", after refusing to rethink the controversial 1% cap on wages for public sector workers.