So many patients are facing long waits for treatment, GP appointments and diagnostic tests that the NHS is "palpably fraying at the edges", the leader of Britain's doctors warns on Monday.

Crucial services are deteriorating because the cash-strapped health service cannot cope with rising demand from patients at the same time as ministers are "attacking the overall financial viability of the service", Dr Mark Porter said.

Porter's intervention comes as research shows that one in four people arriving at A&E are there because they could not see a GP quickly enough. The study was funded by the National Institute for Health Research and collated by researchers at Imperial College London, and is the first of its kind.

It shows that 5.77m attendances at A&E units England in 2012-13 – 26.5% of the total – occurred after patients had tried but failed to get a timely consultation with a GP.

NHS performance could slip further in the next few months because of inadequate funding and ongoing increases in patients seeking treatment, said Porter, chairman of the British Medical Association (BMA), in an interview with the Guardian.

"The year-on-year reduction in resources in many areas is leading to a service that's palpably fraying at the edges," he said. "You have a service that's suffering from a lack of proper investment, constant resource restrictions and cost control, and is demonstrably and noticeably in a number of places starting to fray at the edges.

"The NHS is very much under strain. Waiting times for elective [planned] care are going up, the four-hour target for A&E is deteriorating and hospitals' ability to get patients through properly is being affected. It's not a winter crisis as such but the indicators [of NHS performance] aren't as good as they should be at this time of year. They're looking like winter, even though it's summer," added Porter.

Official figures show that growing numbers of patients are unable to get a diagnostic test such as an MRI or CT scan within the six weeks set out in the NHS constitution, and the waiting-list for operations recently topped three million for the first time in six years.

GPs organisations did not dispute the finding that delays to appointments prompt significant numbers of those with symptoms to opt for A&E. But they said the findings showed that family doctor services were under "unsustainable strain" because of years of under-investment.

"This research is further evidence of the crisis in general practice, with family doctors heaving under the strain of rocketing patient demand, due to a growing and ageing population, and plummeting investment," said Dr Maureen Baker, chair of the Royal College of GPs. General practice's share of NHS funding has fallen from 11% to 8.4% in recent years, even though GPs handle 90% of patient contacts with the NHS and are expected to play an ever more active role in managing many patients' conditions.

Unless general practice receives 11% of NHS funding by 2017, to recruit more GPs and offer more and longer appointments, demand for hospital services will continue to rise inexorably and "the future for patients is looking increasingly bleak", added Baker.

Dr Clifford Mann, president of the College of Emergency Medicine, which represents A&E doctors, put the figure for patients coming to A&E after having difficulty getting a GP appointment at 15% rather than 26.5%, but said that was still 2.1m patients a year. Many more hospitals should have GPs working alongside their emergency department in order to reduce demand on A&E staff, Mann said.

"In the NHS most patients are still getting a good deal, despite the growing pressures. But when you start attacking the overall financial viability of the service, as is happening at the moment, then there's a serious risk that performance will deteriorate. I'm concerned that will happen," added Porter.

Some GP surgeries could close as growing numbers of family doctors are quitting because general practice cannot cope with patients' demands, and some doctors are seeing up to 60 patients a day, he said.

His assessment comes amid signs of growing unease within the government about the NHS, and directly contradicts claims by the health secretary, Jeremy Hunt, in parliament this month that while "operational pressures" meant it was "tough out there … the NHS is now doing extremely well in very challenging circumstances".

Porter's remarks follow Liberal Democrat former health minister Paul Burstow's statement, in yesterday's Observer, that the NHS will need an extra £15bn for the five years from next April "if you don't want the system to collapse during the course of the next parliament".

Although a recent report from the influential Commonwealth Fund think-tank in America rated the NHS as the best and most efficient service out of 11 countries' health systems studied, that may no longer be the case because the NHS has received flat funding while experiencing an ongoing rise in demand in the last few years, Porter said.

A Department of Health spokesperson said: "Everyone should get timely care. We've taken tough decisions to protect the NHS budget and are strengthening family doctoring, reforming out-of-hospital care and improving GP access for 7.5 million people. We are supporting the NHS to ensure urgent and emergency care services are fit for the future and recently pledged an extra £650m to ease pressures."