Analysis by the BMA predicts that more than 4 million patients could be waiting more than four hours to be seen by 2020

A million more patients could face waits of more than four hours in NHS A&E wards in England by 2019-20 in the absence of urgent action to address rising demand, the British Medical Association has said.

Analysis by the doctors’ union, shared exclusively with the Guardian, projects that the number of people attending emergency wards and waiting more than four hours to be treated could reach 3.7 million in three years’ time, up from 2.6 million in the year ending September 2017.

The forecast assumes numbers increase at the same rate as the average over the past five years and a “do-nothing scenario”, in which funding remains at its current level and the proposed measures to address pressures have little or no effect.

If accurate, it would mean 84.8% of patients being seen within four hours between October 2019 and September 2020, down from 89% in 2016-17 and significantly short of the 95% target, which was effectively scrapped by Jeremy Hunt, the health secretary, in January.

The BMA chair of council, Dr Chaand Nagpaul, said: “These alarming figures show the scale of the challenge facing the NHS. As demand increases and waiting times rise, many more patients are left waiting longer for care. It is clear from this analysis that we need urgent action to close the gap between investment and rising demand on the NHS.”

The union also predicts that “trolley waits”, where patients are left waiting more than four hours for a hospital bed after a decision to admit, will more than triple by 2019-20, from 566,000 last year to 1.78 million. It says there could be an average of 5.2 million patients on the elective treatment waiting list by then – up from 3.9 million – for operations such as cataract removal, hernia repair or hip or knee replacement.

Significant increases are forecast over the next 12 months, with the number of people waiting more than four hours at A&E predicted to hit 2.95 million in by September 2018, and the number of trolley waits expected to rise 44% to 816,000.

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Leading doctors have said that already overstretched emergency departments in England could struggle to cope in the event of a major flu outbreak, such as that seen in recent weeks in Australia and New Zealand. They have cited high bed occupancy rates caused by lack of funding, especially in social care, and staff shortages as contributing pressures.

There could be as many as 300,000 people a month waiting more than four hours at A&Es by December, according to the BMA analysis. This could exceed 400,000 by 2020, meaning more than a fifth of patients attending emergency wards waiting more than four hours. The highest monthly figure in 2016-17 was 281,612, in January.

The problems are being partly driven by an expected surge in attendances, predicted to hit 23.8 million over the next 12 months, up 345,000 on 2016-17, and 24.5 million – more than two million a month – in 2019-20.

Nagpaul said: “With the budget less than a month away, the government needs to address the fact we spend about £10bn less per year on health that other leading European economies. Plugging this gap could fund, for example, another 35,000 hospital beds or 10,000 doctors, which could transform patient care.”

A Department of Health spokeswoman described the research as “rudimentary” and said that it oversimplified the trajectory of waiting lists.

“Doing nothing was never an option for the NHS – we have given an extra £8bn investment by 2022, including £2bn for social care and £100m for A&E and last year, the NHS treated 2.2 million more people in A&E within four hours than it did a decade ago,” she said.

“The BMA is wrong to say we spend less per year on health than other leading countries; in fact spending on the NHS is in line with other European countries and our health service has, once again, been independently judged to be the best and most efficient health system in the world.”