Growing numbers of patients are having to wait more than a week to see their GP as family doctors struggle to cope with a relentless increase in people seeking appointments, a survey commissioned by the NHS shows.

More than 26 million people waited at least a week to see a GP in the last year, according to an official survey of the satisfaction of almost a million patients in England.

That is 2.5m more than the 23.6 million who faced the same delay in the 12 months to December 2012 – an annual rise of 10.6%. It is also 4.2m (or 16%) more than the 21.9m who did so 18 months ago, when the results same twice-yearly survey were published in June 2012.

The disclosure brought renewed focus on the coalition's stewardship of the NHS and warnings that A&E units, already buckling under the weight of patients, could not cope with those who turn up because they cannot get to see a GP as quickly as they would like.

The findings emerged from a Royal College of GPs analysis of the findings of the most recent GP patient survey, which NHS England issued this month, and its predecessors in June as well as December and June last year.

The number of people left waiting at least seven days is likely to rise again next year to about 27m, the Royal College said. "These figures are hugely concerning, for patients and GPs. They demonstrate an emerging crisis in general practice that could be as bad, or worse, than that in A&E," said Dr Maureen Baker, RCGP chair. "If waiting times get longer it will be more difficult for GPs to ensure that problems are caught early, and the pressure on A&E will intensify. This is bad news for patients and bad news for the whole of the NHS."

Lengthening waiting times were the result of GP numbers not keeping up with demand and NHS bosses giving general practice an ever-smaller proportion of the service's £110bn budget, Baker said. She said the NHS urgently needed to recruit 10,000 GPs across the UK and reverse a shift in resources which has seen general practice's budget share fall from 11% in 2005-06 to 8.4% in 2011-12 at a time when the budget rose by 18%.

Andy Burnham, the shadow health secretary, said it was "simply not acceptable that any patient should have to wait a week or more for a GP appointment."

The most recent survey, of 943,000 patients, found that 15% of the 317m who sought an appointment with a GP or nurse this year – or 46.8 million people – had to wait at least a week, 1% more than a year earlier and 2% up on the proportion found in June 2012. That is likely to rise to 48.4m in 2014, Baker said.

Some findings were positive for patients, such as the slight rise from 36% to 37% in the number of patients who got an appointment on the same day they rang the surgery. However, slightly fewer patients – 13%, down from 14% in 2012 – were seen on the next working day.

Similarly, there was a slight fall in the number of patients seen a few days later, from 33% to 32%, and the 1% rise in the number seen a week or more later.

The RCGP also released figures showing that the number of hospital consultants has overtaken that of GPs in the NHS, even though services are meant to increasingly be provided in community settings, including GP surgeries. Three consultants are being recruited for every new GP, said Baker, who criticised the fact that hospitals are receiving an ever-larger share of NHS funding.

"Under David Cameron, it has got harder to get a GP appointment", Burnham said. "Now it looks like things will get worse in 2014 and people will face even longer waits, adding to the growing pressure on A&E. Next year, more and more people will be calling the surgery at 8am only to be told nothing is available for days."

The coalition's scrapping of the guarantee Labour gave patients that they would see a GP within 48 hours was "a major mistake" which should be reversed, he said.

Dr Chaand Nagpaul, chair of the BMA's GPs committee, said: "GP practices are under intense pressure from a combination of rising patient demand, especially from an ageing population, and declining funding.

"In the current climate, GP services are being asked to do more with less, despite the government acknowledging that more care will in the future need to be delivered in the community by GPs.

"Workload pressures are also leading to low morale and stress in the current workforce, undermining our ability to recruit and retain GPs."

Dan Poulter, the health minister and a hospital doctor, said the survey showed 86% of patients said their overall experience of their GP practice was good.

"We have announced a £50m fund to support innovative GP practices to improve access for their patients so that people who lead busy lives will have better access to GP services when it suits them. The new GP contract introduces same day phone consultations for the most vulnerable patients on practice lists.

"The health secretary has said clearly that he wants to give elderly people a dedicated GP, personally accountable for their care around the clock, and bring back the era of the family doctor."

The GP workforce will be boosted because ministers have ensured 50% of medical students will become family doctors by 2020, Poulter said.