Bupa has drawn the ire of Australia’s peak medical body after informing doctors insured patients would qualify for gap cover only if they were treated in a Bupa-approved hospital or medical centre.

Last week the health insurance giant was subjected to a backlash from members when it told a third of them their policies would no longer cover major surgeries such as hip and knee replacements.

The president of the Australian Medical Association, Dr Michael Gannon, said Bupa’s decision to determine which hospitals patients were sent to was “not at all” acceptable.

“The reason we worry specifically about Bupa is not only are they the insurer holding the greatest number of polices and the biggest player in the game, they are the closest to being able to have contracts with doctors that force doctors and patient to use Bupa hospitals,” he told Guardian Australia on Tuesday.

“That is US-style care and it will be resisted by our profession at every level. We can’t have a situation where an insurer decides what care patients can and can’t get. Bupa already owns dental facilities, and to have complete control they’d own hospitals and employ doctors.”

The health system functioned most effectively when doctors and hospitals operated as independently as possible from the insurers, Gannon said.

The Bupa medical gap scheme is designed to eliminate or significantly reduce medical costs associated with hospital treatment by paying doctors significantly higher benefits than those paid under Medicare. Insured patients can currently choose which hospital they receive their treatment at, including at any public hospital their surgeon may work at.

But in a letter to doctors, Bupa announced that from 1 August: “The higher scheme benefits will only apply when participating providers choose to use the scheme at hospital facilities that have an agreement with Bupa.”

Dr Fred Betros, a general surgeon operating in western Sydney, took to Facebook to share his frustration about the changes and the impact on his patients. His post, which has been shared almost 9,000 times, states: “I’m a doctor, but at times both me and my family are patients as well. I always want to have a complete choice and I don’t want a non-medical person deciding what is best for me. I was a Bupa customer until yesterday”.

The foreign-owned Bupa made 49% of its worldwide profits from Australia and New Zealand in 2016, its most recent annual report shows.

However a Bupa spokesman said Gannon’s claims that Bupa was heading towards a US-style system were “absolutely false”.

“Doctors, never health insurers, will always determine patients’ treatment and care options as they do today; nothing has changed. The doctor’s right to do so is protected by legislation,” the spokesman said. “However, customers have been asking for greater clarity on costs especially at locations where mixed arrangements were in place, and this change to the medical gap scheme is designed to support this.

“Managed care cannot and will not occur in Australia. This is complete misinformation. The only change, applicable only at a very small number of locations, actually means doctors must advise a patient if they are going to a contracted hospital or not, and then must advise what their medical costs will be for the service.

“The patient then will have full informed consent and can decide how they wish to proceed … It’s also important to know this change only impacts a very small portion of Bupa claims.”

The federal health minister, Greg Hunt, on Tuesday ordered the Ombudsman to investigate Bupa over the changes.

The latest State of the Health Funds report from the commonwealth ombudsman said private health insurance complaints had increased significantly over the past four years.

“In 2016-17, we received 5,750 private health insurance complaints, compared to 4,416 in 2015-16,” the report said. “This is an increase of over 1,300 complaints within one year, which is the largest rise we have experienced over the past 10 years. Consumers experienced increased problems associated with benefits, service, written information, verbal advice and health insurance membership administration.”

The chief executive of the Australian Healthcare and Hospitals Association, Alison Verhoeven, said the escalating numbers of complaints about private health insurance provided further proof that a Productivity Commission inquiry was “urgently needed”.

This would help policy makes understand “how we can get better value for the $6.5bn taxpayer subsidy for private health insurance businesses, and for people who have purchased insurance”, she said. “This should be part of an overall shift in focus to value-based healthcare.”