But the proposal has sparked concerns from consumer advocates and health economists that such a change could accelerate a shift to a two-tiered health system, where those who can afford private cover receive better care than those who don't have insurance.

In November, Medibank Private began a trial with medical centre manager IPN in which six of its Brisbane medical centres will provide Medibank members with a range of enhanced GP services – including a guaranteed appointment within 24 hours and after-hours home visits – for no out-of-pocket costs. Medibank is not paying IPN for the services directly but is contributing to the "administrative and management costs" of the trial.

Dr Washer, who retired at last year's election after 15 years in politics, said he thought allowing insurers to pay gap fees for GP services was "a bad idea," because doctors could increase their fees knowing their patient would not have to pay, and there would be no price signal to patients to deter them from visiting the doctor unnecessarily.

But Dr Washer said the cost of these services would have to be met by health funds, who would pass the costs on to their members in higher premiums. Ultimately, even uninsured taxpayers would bear part of the burden of these higher costs through the private health insurance rebate.

Dr Washer backed a proposal being considered by the Abbott government's Commission of Audit, for a $6 fee to visit the GP. The author of the proposal, Terry Barnes, a former advisor to Tony Abbott as health minister, predicts the fee would save $750 million over four years by reducing "avoidable" demand for GP services.