Health experts have said the chancellor’s £20.5bn boost for the NHS in England by 2023 will leave the service still struggling to cope with rising demand for treatment.

The pressure on already overloaded A&E and GP services will continue because Philip Hammond only gave an extra £650m to prop up crumbling social care services, it was claimed.

Theresa May has promised the £20.5bn increase in NHS funding over the next five years will yield major improvements in cancer and mental health care. But doubts were raised about how much progress to expect.

“After a financial squeeze of many years, much of this new money will be needed just to get the basics back on track – keeping up with rising need, addressing sliding [treatment] waiting times and fixing the worrying backlog of buildings needing repair,” said Prof John Appleby, the chief economist of the Nuffield Trust, a health thinktank.

“Our calculations show that after meeting the commitments already made to patients, only £500m will be free next year for any improvements – less than a tenth of the headline increase.”

Health, NHS and older people’s organisations said the £650m was enough only to “stave off total collapse” of social care services and amounted to “a sticking plaster” given the scale of unmet need.

Prof David Oliver, clinical vice-president of the Royal College of Physicians, which represents hospital doctors in England, said the rise “can only go a small way to alleviating the pressures places upon the NHS by having to care for people in hospital who would be better looked after in the community”.

Niall Dickson, chief executive of the NHS Confederation, which speaks for NHS trusts, said the £650m was “clearly inadequate” and would lead to social care remaining “the achilles heel” of the system. Appleby said the money was “another short-term fix to a system nobody seriously disputes is fundamentally broken”.

The King’s Fund, Age UK and Alzheimer’s Society urged the government to replace its annual injections of emergency cash for social care with a plan in a forthcoming green paper to ensure the system’s viability in the long term.

Hammond said the £20.5bn was an “extraordinary commitment” which reflected the view that “our NHS is the number one priority of the British people”. Announced just before the NHS’s 70th birthday in July, it will increase NHS England’s budget from £115bn this year to £135bn by 2023/24.

He was accused of issuing misleading figures by claiming in his speech to MPs that the government was giving the NHS an “£84bn” boost over the next five years. That sum includes the extra sums the NHS in Scotland, Wales and Northern Ireland will receive for health as a result of the Barnett formula.

Mental health organisations welcomed Hammond’s confirmation that NHS mental health services in England would receive “at least £2bn” more in real terms by 2023/24, fulfilling a commitment to give mental health an increasing proportion of the NHS’s overall budget.

It will pay for improvements such as every A&E unit in England having specialist mental health staff on duty around the clock, greater support for troubled children and young people, and more services for people in crisis.

However, the Royal College of Psychiatrists said the true amount of extra cash needed by NHS mental health services by 2023/24 was £3.7bn, almost double Hammond’s £2bn.

That was the sum needed to pay for the recruitment of large numbers of extra mental health nurses, therapists, psychiatrists and support workers to respond to rising demand and meet new waiting time targets, the college said.