Only around one in five GP surgeries offers extended hours to patients seven days a week, official data shows.
The Government has committed to improving access to GPs in the evenings and weekends through surgeries putting on extra sessions where appointments can be pre-booked.
Previous research has suggested that demand from patients for weekend appointments is low but the Department of Health says that as weekend opening becomes "normalised", it expects demand to grow.
The new survey of just over 7,000 GP practices for NHS England found that 6,164 practices (86% of the total) provide partial or full extended access, covering 49.51 million patients in England.
Partial access could mean anything from one extra 1.5 hour session after 6pm on one day per week, to six extra sessions a week or Saturday opening. Practices can also work as groups to offer the sessions to their patients at another practice if theirs is closed.
The survey found that around a third of practices provided extended opening on one or two days per week.
But full extended access across seven days was only available at 1,318 (19%) practices or another practice within the local group. This is despite former prime minister David Cameron pledging that patients would be given access to GPs seven days a week by 2020.
Some 975 practices, which provide care to 6.4 million patients, were found not to provide any access to appointments outside normal working hours.
The survey found that the most common offer from practices was a later opening on one day of the week. The second most common offer was extended access on all seven days of the week.
Sunday was the least common day for practices to offer extra appointments.
An NHS England spokesman told the Health Service Journal (HSJ), which first reported the story: "We know just how much the public value a timely GP appointment, so it is encouraging to see from these figures that local GP practices, by working together, are offering evening and weekend appointments to the vast majority.
"These figures confirm that the best approach for offering extended access is not for each practice to have to do so on its own, but instead to share appointments across practices."
In October 2015, an official review found there was "very low" demand for Sunday appointments.
Patients also snubbed appointments on Saturday afternoons, although Saturday mornings and weekday evenings proved more popular.
The review examined data from 20 pilot sites across England - covering 1,100 general practices and 7.5 million patients - which were testing seven-day services.
The report, from independent consultancy firm Mott MacDonald, found there had been some success with the scheme, including better use of weekday GP time.
But it said there had been low up-take of weekend appointments compared with weekday ones, particularly on Sundays.
As a result, some sites had cut their weekend appointments to just a few hours, while others ceased to offer any extended hours appointments.
Katherine Murphy, of the Patients Association, told the Daily Mail of the latest figures: "We are disappointed to hear most areas are still falling behind in offering GP appointments at evenings and weekends ... If patients do not have access to primary care services they are more likely to attend A&E departments, which are already experiencing high demands.
"Lack of access to GPs is of significant concern. Long waits are unacceptable as some patients may decide not to seek treatment ... This may lead to serious illnesses being missed."
Professor Helen Stokes-Lampard, of the Royal College of GPs, said: "Extending GP surgery opening hours means taking staff and other resources away from our routine service, which is already stretched incredibly thinly due to years of decline in investment."
She added that many practices offering services in the evening and at weekends have stopped because "patient demand has been so low".