Rishi Sunak hopes a “blueprint” inspired by the coronavirus vaccine rollout will help tackle the NHS’s four “healthcare missions” of cancer, obesity, mental health and addiction.

The prime minister has announced more than £113m in funding for research into new treatments and technologies with the aim of encouraging breakthroughs.

Ministers believe tackling the key challenges could save the health service and the economy billions, with obesity alone estimated to cost £6.1bn a year.

But the NHS is also struggling with a record treatment backlog and staffing crisis, with nurses preparing to strike next month over pay and patient safety.

The British Medical Association welcomed the “injection of funding” for research but warned it must be coupled with further investment in the NHS and in the welfare system.

Medical academic staff committee chairman Professor David Strain said: “Doctors are already struggling to pick up the pieces of a broken social safety net.

“A stronger social safety net, backed by well-funded public services, would save thousands from needing the NHS’s services at all.”

Prof Strain said the government needs to invest more in the NHS “here and now” – saying the extra £3.3bn of funding announced in the autumn statement was an “effective pay cut to the health service’s budget”.

“This is impeding the NHS from getting on top of the backlog and providing treatment to patients who desperately need it, causing untold suffering across the country.”

In his autumn statement, Chancellor Jeremy Hunt promised an additional £3.3bn in funding for the NHS for each of the next two years.

But nearly all of that will be eaten up by the costs of inflation and growing demand, with just £800m left over for the improvement of services, according to analysis by the Nuffield Trust.

Mr Sunak, Health Secretary Steve Barclay and Business Secretary Grant Shapps will meet NHS leaders, global chief executives and key industry figures on Monday.

“The NHS faces real pressures, which is why we are investing over £100m in the technologies and medicines of the future to address some of the biggest public health challenges facing our country,” Mr Sunak said.

The government hopes to follow the vaccine approach with its “missions” by harnessing the best research expertise, removing unwarranted bureaucracy and strengthening partnerships with businesses.

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Research into mental health will get £40.2m, addiction £30.5m, cancer £22.5m and obesity £20m.

Each mission will be led by an independent expert, who will be chosen by a panel that will include Dame Kate Bingham, who headed the vaccine taskforce.

Shadow health secretary Wes Streeting said: “It is welcome that NHS and life sciences leaders are being brought in to help fix the mess the Conservatives have made.”

Liberal Democrat health spokeswoman Daisy Cooper said the “level of ambition for health research is long overdue”.

“But as health and care services prepare for one of the most difficult winters in memory, the government needs to urgently demonstrate this level of ambition when it comes to GP appointments, ambulance delays, discharges to social care and hospital beds,” she added.

“Our health and care services are stretched to the brink of collapse after years of mismanagement by this Conservative government.”