Of the GP patients in the Doncaster CCG who responded to the NHS's annual GP survey, 19 per cent said they had to wait a week or more to see a doctor or nurse last time they booked an appointment.
Five years ago, just 12 per cent of respondents had to wait that long.
The Royal College of GPs said the findings were concerning, and that there is a risk of people not getting the treatment they need to prevent medical conditions becoming more serious.
Professor Helen Stokes-Lampard, chair of the Royal College of GPs, said: “Patients are still waiting too long for a GP appointment, and too many are not getting an appointment when they want one.
“The truth is that GPs and our teams are working to absolute capacity and we just don’t have enough GPs to offer enough appointments."
More patients of Princess Medical Centre, Woodlands, reported long wait times than at any other GP surgery in Doncaster. Here, 57 per cent of patients said they had to wait a week or longer for an appointment. At the other end of the scale, only one per cent of patients faced a week's delay at Regent Square Group Practice, Town Centre.
Professor Stokes-Lampard added: “Health Secretary Matt Hancock has identified workforce and prevention as two of his top priorities and if he is serious about tackling the GP workforce crisis, and keeping patients out of hospital where care is far costlier, it is essential that the Government invests properly in general practice."