Jeremy Hunt has been told to come out of hiding and stump up the cash to end the NHS strikes.
The tight-fisted Chancellor is refusing to provide extra funding so nurses and ambulance workers can get a proper pay rise.
Paul Nowak, the new head of the Trades Union Congress, accused Mr Hunt of being “missing in action”.
The general secretary argued “there has to be more money [made] available” to end the walkouts across the public sector.
Ministers have held talks with union leaders, but he argued their “hands are being tied” by the Chancellor.
"We are on the hunt for Hunt,” he said. “The Chancellor and Prime Minister are the key to unlocking the disputes, but they have been invisible.
"It's good that meetings are taking place, but ministers' hands are being tied by the Treasury and No 10."
Mr Nowak, who took up his job at the beginning of this year, has written to Mr Sunak to demand a meeting but he has not had a response.
“There's a startling lack of creativity and imagination from government,” he added. “You’ve got to sit down and negotiate.
“It has been incredibly frustrating that it was only this week that the government even began to have a conversation.
“I can't think of a private sector employer who would effectively stonewall their own staff for six months who want to talk to them about pay.”
Health Secretary Steve Barclay is considering options to break the deadlock.
Ideas that have been floated include a one-off payment for NHS workers or back-dating a pay rise due to come in later this year.
Up to 25,000 ambulance workers across England and Wales took part in walkouts on Wednesday. Nurses are due to take part in further strikes on Wednesday and Thursday.
But the Prime Minister today dismissed calls for the NHS to get extra funding to end the strikes.
Despite the health service teetering close to collapse with patients facing record waits, Mr Sunak insisted it is receiving "record funding".
Asked whether there will be more money to improve hospital staffing levels, he told BBC Radio Scotland: "There are challenges that the NHS faces as a result of recovering from Covid in every part of the United Kingdom.
“What everyone needs to know is there is record funding already going into the NHS and most recently in the autumn statement in spite of the difficult but fair decisions we had to make to get a grip of borrowing and tackle inflation."
Mr Sunak held talks with Nicola Sturgeon on Thursday evening. The First Minister said there was "no indication from the Prime Minister of new money" to avert strike action within the NHS.
The Prime Minister’s spokesman said: “We've been clear from the outset that departments have received the funding allocations and it remains the case that pay rises would have to come from those allocations.
“It's obviously not for me to set departmental budgets going forward that would be entirely a matter for the Chancellor.”
During his visit to Scotland on Friday, Mr Sunak said: "I think with strikes it's important that we remain in strong dialogue with the unions, that's why the Government invited all union leaders in to have those discussions.
"The discussions are ongoing and hopefully we can find a way through."
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