More than one in three patients has to wait at least a week to see a GP, and one in seven cannot get an appointment for between two and four weeks.

Research suggests that general practice is at “breaking point” as rising demand forces 34% of people to wait a week or more for a consultation.

A survey of 4,022 adults in England, Wales and Scotland, who form a cross-section of the population, found that 17% get an appointment within one to two weeks, 11% face a wait of two to three weeks, 4% wait three to four weeks and 2% cannot get one for at least four weeks.

The findings underline the scale of the task facing Boris Johnson who pledged to cut waiting times. “General practice in England is in crisis. The system is at breaking point. Patients are unable to access the care they need when they need it most,” said Harry Quilter-Pinner, a senior research fellow at the IPPR thinktank, which commissioned the survey from Savanta ComRes.

More positively, though, 19% said they got an appointment on the same day, 15% within one or two days and 21% between two days and a week.

However, people with a long-term mental or physical health condition or a disability had to wait longer than others. Of those, 43% had to wait longer than a week. These are “shocking” findings, said Quilter-Pinner.

And only small numbers of patients are getting a longer appointment to discuss their health (16%), or a personalised care plan (7%), education or training about how to manage their illness (4%) or a “social prescription” – access to non-medical treatments such as social activities (3%) – even though the NHS long-term plan in England has prioritised such interventions.

“It is totally unacceptable to expect patients to wait weeks for a GP appointment. Patients – and GPs – deserve more,” said Professor Martin Marshall, chair of the Royal College of GPs. “Over 1 million patients are seen in general practice every day, but our service has been running on empty for too long and one of the consequences is that we now have a severe shortage of GPs.” There is scepticism about Johnson’s promise to recruit 6,000 more.

The survey also found that 69% of respondents want GPs to be directly employed by the NHS. They have been independent contractors since the health service was created in 1948 and the IPPR says this model must be scrapped in order to improve general practice.

The Department of Health and Social Care said: “The latest NHS figures show 40% of all appointments take place on the same day they are booked, with millions of patients already benefiting from more convenient evening and weekend appointments. By expanding the workforce, harnessing technology and giving GPs the support they need, we will create an extra 50m general practice appointments a year, helping to reduce waiting times.”