The NHS needs to do more to cut waste and put funding back into frontline care, Philip Hammond said following criticism that his Budget did not allocate enough to England’s health service.

Health chiefs are to meet to discuss “what it is possible to deliver for patients with the money available” after the NHS did not get the funds it requested from the Treasury, officials have indicated.

The Treasury pledged more money for the NHS in England, with the specific aim of helping the health service “get back on track” with soaring waiting lists and A&E targets.

Mr Hammond committed resource funding of £2.8 billion to the NHS in England.

This includes £350 million to cope with pressures over the coming winter, £1.6 billion in 2018/19 and the rest the year after.

Mr Hammond said the efficiency plan set out by NHS England chief executive Simon Stevens had not yet been fully implemented and more savings could be made which could fund patient care.

“Simon Stevens set out a five-year plan for the NHS in 2014 which we funded in full and that five-year plan has not yet been delivered,” he told ITV’s Good Morning Britain.

“The NHS have come back and said, ‘look, demand has been higher than we expected, we need some more money’, and we have put some more money in.

“We will continue to work closely with the NHS management and the Department for Health to make sure that we cut out waste in the service, that we focus the money that is available on the frontline on delivering for patients and we get the outcomes that the NHS five-year plan said it could deliver over that period of time, that’s what patients want to see.”

He told Sky News the five-year plan “set out to transform the way the NHS works, to make big efficiencies in the way it operates that could then be recycled to the frontline to provide additional patient care”.

“That plan hasn’t yet been fully delivered and we have agreed to put some additional money in to support it,” he said,

Tory MP Kwasi Kwarteng, who is parliamentary private secretary to the Chancellor, said it was possible the NHS could receive the extra £350 million per week promised by Leave campaigners during the referendum.

He told BBC Radio 5 Live: “That’s what was said on the side of the bus. And I think actually that we could deliver that. That’s my own view. That’s a personal view.

“Once we have finished that (Brexit) process – once we’ve finished up to 2019 and the transition process – I think there would be money that was freed up, which would be to the tune of probably about £10 billion a year.

“And because the economy is growing, we would be able to spend a lot more of that money on the NHS. It will be up to the Government to decide the exact amount.

“We spend £350 million a week now for our EU contributions. Now, when that ends, we will have that money. And it would be possible, if you were a chancellor or someone leading a government, to use that money on the NHS.

“All those things are incontestable. That is the truth.”