Labor has criticised the size of private health insurance premium rises after reports that up to half a million Australians may drop their cover.

This month the government announced it would approve private health insurance premium rises of 5.59% on average from 1 April, slightly less than the 6.2% demanded last year. The price increases will cost about $200 a year for families and $100 a year for singles.

Those rises could prompt more than 530,000 Australians to drop their private health cover, according to a Galaxy poll commissioned by the health fund comparison site iSelect.

“It’s possible these households have already pared back their cover as premiums have risen in recent years but this latest increase may be the tipping point that means they can simply no longer afford it,” said an iSelect spokeswoman, Laura Crowden.

The figure of half a million represents 7% of those with private insurance. If that occurred it would be a drop far in excess of falls of just 0.2% of all private policy holders in the quarter to December 2015.

On Monday the acting opposition leader, Tanya Plibersek, said when she was health minister she would send back insurers’ “ambit claims” to force them to reconsider. “That meant on average under Labor, under both Nicola Roxon and I, premium increases were below the averages that we’re seeing under Liberal governments,” she said.

Plibersek based the claim on statistics that show the average increase in premiums under the Abbott and Turnbull governments was 5.99%, compared with 5.5% under Rudd and Gillard and 6.67% during the last six years of the Howard government.

But in Labor’s last year in office, premiums rose by 5.6% – higher than this year’s result.

Plibersek said: “The health minister does have the power to reject increases and the government needs to consider what happens to people who have private health insurance when it becomes so unaffordable.”

The health minister, Sussan Ley, told Guardian Australia: “Health premium rises in 2016 are at a four-year low after record number of health insurers resubmitted lower health premiums at my direct request.”

In total 20 health funds resubmitted a lower increase when prompted by the government, with some cutting back as much as 1.5%, easing costs for more than 93% of Australians with private health cover. “Consumers will be $125m better off as a direct result of our request for insurers to resubmit lower premiums,” she said.

“Consumers haven’t forgotten Labor’s $3.5bn cuts to the value of their private health rebate, which pushed up premiums even further for millions of Australians.”

Ley said a government survey of 40,000 Australians found a majority raising concerns about the affordability of their premiums and the value for money they received from their policies.

She said private health insurance had to continue to deliver value for money as it was “a fundamental element of our health system that offers consumers greater choice while taking pressure off of Medicare so that its universality remains sustainable”.