Figures obtained by the Yorkshire Post have found half of new flagship access centres in the region are seeing at least double numbers of walk-in patients expected.
One surgery in Bridlington saw nearly seven times as many people in its first year as predicted.
Demand is three times the level expected in Bradford and at least double in Grimsby, Scunthorpe and two centres at Halifax and Todmorden in Calderdale.
Barnsley's walk-in service has already been axed after more than four times the numbers expected sought care in its first 15 months and hours at another centre in Dewsbury have been cut as health chiefs struggle to meet costs.
Campaigners say their success offering on-demand appointments from 8am-8pm each day highlights the difficulties patients face in getting quick appointments with their own GPs. But there are growing concerns they could be a victim of their own success as NHS chiefs face budget cuts.
The access centres opened by Labour were opposed in a national campaign by family doctors who claimed money could be better spent on existing services.
The Bridlington centre was expected to have 150 walk-in patients each month but average figures show more than 1,000 people visited it monthly in its first year.
Around 540 patients a month were due to visit the centre in Bradford but figures show 1,530 have used it on average.
The Barnsley centre was due to see 5,000 patients in the 12 months until next July but had already exceeded this by October.
In Dewsbury, demand was double that expected, generating extra costs it was estimated would approach half-a-million pounds over a full year.
Katherine Murphy, chief executive of the Patients Association, criticised health chiefs for closing popular services.
"Here we have another example of a knee-jerk reaction by primary care trusts (PCTs) who should be publicising the effectiveness of walk-in centres instead of closing them," she said.
"Rather than scrapping these walk-in centres or slashing their opening hours, PCTs and the Government should be asking themselves why they are so popular.
"Patients do not want to have to wait for an appointment or take time off work to get into a surgery. They want ease of access to their GP at a time which suits them and if they don't get it at a normal GP practice they will look for it elsewhere."
David Rose, managing director of Primecare which runs centres across the country including Barnsley and Scarborough, said walk-in health centres had proved really popular with patients "because they provide exactly what people want. Good access, at a time to suit the patient, with a choice of healthcare professional and being made to feel welcome at the centre is why this type of service is a success."
But Leeds GP Richard Vautrey, deputy chairman of the British Medical Association's GP committee, said the walk-in centres were duplicating existing services and were not good value for money. The "vast majority" of people they saw were seeking help for illnesses which did not need treatment.
He added: "GPs do their level best to provide quick access to those with a clinical need."
Bosses at NHS East Riding of Yorkshire said they had "no immediate plans" to change the Bridlington service but periodical reviews were carried out.
Officials at NHS Barnsley said the worsening financial climate meant they could not afford to keep the centre open to walk-in patients who could instead see their own GP
NHS Kirklees said the reduction in hours at Dewsbury would "help to use NHS resources as effectively as possible".
staffing cuts 'could cause deaths'
Patients could die because of staffing cuts in the NHS, says Britain's nursing leader.
Dr Peter Carter, general secretary of the Royal College of Nursing, said the Government's planned 20bn of NHS efficiency savings were causing "some of the most widespread cuts in its history".
There was an "indisputable link" between staffing levels and mortality rates.
Dr Carter said: "The worry is that we have seen time and again what happens when staffing levels are slashed without thinking of the impact on patient care."
A spokesman for the Department of Health said reform was necessary.