Britain’s top GP has said surgeries will have to stop seeing patients during the week unless ministers abandon their drive to guarantee access to family doctors at weekends.

Dr Helen Stokes-Lampard condemned the policy, a key Conservative pledge, as unrealistic and said it was ignoring the lack of demand among patients to see GPs at weekends and a serious shortage of family doctors.

The government has promised to ensure that people in every part of England will be able to see a GP from 8am to 8pm every day of the week by 2020 as a key element of its push to create a “truly seven-day NHS” by the end of the current parliament.

“It’s unrealistic in the current climate. We haven’t got the people, we haven’t got the resources. If you give people access on a Sunday afternoon they’re not going to have access on a Tuesday morning. They can’t have it all”, the chair of the Royal College of GPs said in an interview.

Calling for surgeries weekend opening to be restricted to Saturday mornings, Stokes-Lampard said: “We should be responding to what is needed in an area, and balance that realistically by what can be provided safely. Because quite frankly if you open on a Sunday afternoon but you’re closed on a Tuesday morning, who’s going to benefit?.

There is so little demand from patients to see a GP on Sundays that plans to compel at least one surgery in each area to open on that day by 2020 should be dropped, she said. Nor do many people want to attend a surgery on a Saturday afternoon, she added.

David Cameron pledged access to GPs from 8am to 8pm seven days a week at the Conservative party conference in 2014, and established a £50m “challenge fund” to deliver it. Some surgeries that have begun opening at weekends, however, have scrapped their experiment because of the small numbers of patients seeking appointments on Saturdays and Sundays.

A relentless rise in the need for care is prompting more GPs to retire early or move abroad, leaving the profession facing a growing workforce crisis and patients facing long waits for appointments, Stokes-Lampard said. As a result “we’re layered too thin at the moment, we’re spread too thin. We can’t sustain a good five-day service at the moment, a seven-day service is unrealistic. If we can’t provide eight to six Monday to Friday because we’re stretched to breaking point, we’re certainly not going to be able to provide seven days a week.”

She said general practice was “closer to the edge than it has ever been in living memory”, and cast serious doubt on ministers being able to fulfil another key NHS pledge – to increase the number of GPs in England by 5,000 by 2020 compared with 2015. It will be very hard to deliver that number without many GPs coming from overseas or former doctors being persuaded back into work, she said.

The Liberal Democrat MP Norman Lamb, who was a coalition health minister until May 2015, denounced the pledge of access to GPs all day and every day as a “superficially attractive gimmick”.

“This target is driven by seductive headlines, not sound policy. It will distort priorities and resources away from action which could make a real difference to people’s lives, such as ensuring that people have both their physical and mental health needs effectively met in primary care,” he said.

“No one believes that there will be sufficient resources to deliver this plan. The risk is that it will leave dangerous gaps in provision during the week.

“Pursuing superficially attractive gimmicks like this amounts to a smokescreen for the dire threat the NHS and care system now faces as it is starved of the resources it needs to provide effective, prompt and safe care.”

The shadow health secretary, Jonathan Ashworth, said: “These serious doubts about a flagship government pledge will raise widespread concerns. It’s yet another warning about the scale of the underfunding and understaffing now impacting our NHS.

“In her six months as prime minister Theresa May has shown no regard for the state of the NHS, so it’s no surprise it now looks like her own manifesto commitments will be broken.

“But in 2017 the government simply must not carry on ignoring the warnings. Instead they need to come forward with a genuine plan to give the NHS and social care the resources they need to deliver the very best care every patient deserves.”

The Department of Health insisted the government would achieve its ambition of seven-day opening, and that the policy was popular. “This is a common sense reform with wide public support, and one we will deliver”, a spokeswoman said.

“People don’t just get ill Monday to Friday, nine to five, and 18 million patients now have weekend and extended access to a GP, which has already shown evidence of relieving pressure on other parts of the NHS.

“To deliver our pledge, we are putting an extra £2.4bn into GP services, which will help expand the workforce.”