Family doctors are demanding an emergency cash injection of £2.5bn to help struggling surgeries cope with demand and offer patients appointments within a reasonable time.

Leaders of the profession want NHS bosses to plough some of the extra £20bn health funding pledged by Theresa May into improving the services offered by England’s 7,150 GP practices.

The Royal College of General Practitioners (RCGP) is warning that waiting times for consultations will lengthen and the care patients receive will suffer unless NHS England agrees the cash boost.

Under current plans, GP services are due to receive £12bn of the NHS budget by 2020-21. But the RCGP believes that should be revised to £14.5bn.

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The money is needed to help with the growing demand to see a GP, a rise in long-term illnesses such as diabetes, and a growing shortage of family doctors, the college said.

In his first speech last month as the health and social care secretary, Matt Hancock identified improving the NHS workforce and redoubling efforts to prevent illness as key priorities. Prof Helen Stokes-Lampard, the chair of the RCGP, said that backing the college’s £2.5bn plea would demonstrate his determination to do both, given GP understaffing and their central role in promoting good health.

“If he is serious about tackling the workforce crisis and keeping patients out of hospital, it is essential that the government invests properly in general practice,” she said.

The GP Forward View policy document published by NHS England in 2016 pledged to increase the proportion of the NHS budget going into GP services to at least 10% by 2021. However, without upping total investment to £14.5bn by that date, its share will fall to 8.9%, Stokes-Lampard added. “It is now time for us to go above and beyond the original GP Forward View,” she said.

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“The vital importance of general practice must be recognised as decision-makers draw up plans as to how to spend the new money that the prime minister has promised the NHS.

“We believe that at least £14.5bn is necessary – an extra £2.5bn a year on top of what has been promised. Only then will we be able to continue to guarantee the safe care our patients need and deserve, close to home where they want it most, away from hospitals where care is more expensive.”

There are 1,000 fewer GPs in England than there were in 2015, despite Hancock’s predecessor Jeremy Hunt’s repeated pledge to increase their number by 5,000 by 2020.

The college’s plea came as it published its second annual assessment of the GP Forward View. It welcomes the “good strides in some areas”, including record numbers of trainee GPs, a ministerial pledge to bring in a state-backed medical indemnity scheme for GPs in England and the placement of pharmacists in GP surgeries to help ease the strain on family doctors. The latter scheme is on track to deliver more than the 1,500 pharmacists promised by 2021.

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But it warns that “general practice has become even more challenging in the past two years”, with workloads even heavier as a result of growing problems of recruitment and retention of GPs, with more choosing to quit early, sometimes in their 50s.

Don Redding, the director of policy at National Voices, a coalition of health charities, did not endorse the £2.5bn demand but said more NHS funding should go on community-based health services to help meet the needs of the ageing population.

“It’s essential to have GP services at the centre of a new NHS service offer that brings care closer to home and supports people to manage their condition succesfully and stay out of hospital as much as possible,” he said.

“Therefore, services outside of hospitals should get an ever increasing share of the NHS budget over the next 10 years in order to make the NHS more patient focused, more effective and more sustainable.”

A spokesperson for the Department of Health and Social Care said: “We recognise the invaluable contribution of GPs and we are determined to support them in every way. That’s why we’re investing an extra £2.4bn a year into general practice by 2020-21 and a record number of doctors are in training.

“As part of our long-term plan for the NHS, we are increasing overall funding by an average of 3.4% per year, meaning that by 2023-24 it will receive £20.5bn a year more than it currently does.”