They recoup part of their payments by asking policyholders who have already met part of their medical bills to fill in and backdate an E111 form. The form is used to claim, on the policyholders' behalf, any money that they might have been entitled to from that source.
Policyholders are told that if they fail to fill in the form, as requested by insurers, they could invalidate the terms of the cover they took out with the insurer.
Jeremy Warner, a journalist with The Independent, was hurt in a skiing accident and had to pay for his medical treatment while abroad.
When he claimed on his return to the UK, he was told to sign an E111 form on behalf of the insurance company. Mr Warner says: "It is pretty scandalous: taxpayers are in effect subsidising the profits of insurance companies."
E111 forms entitle UK citizens to recover from the Government a large share of emergency medical expenses incurred when using any European state health provision. Likewise, other European citizens can do the same in the UK, in theory. The agreement is geared so that EU states offer each others' citizens the minimum health-care available free to the local population in each country, with any extra paid by travellers themselves.
But although the individual's right to claim is waived if a private travel insurance policy is called upon to pay out, insurance companies are stepping in to claim the policyholder's entitlement.
Mr Warner's insurance was taken out through American Express, which places the cover with Europ Assistance.
When he objected to being asked to sign the E111 form on behalf of the insurer, he received a letter from the company. "It is a basic principle of insurance that the insured has a duty to minimise any claim and that insurers will seek recovery of costs wherever possible," it said.
"This would be the case on any type of insurance, not just travel policies. Such procedures do not normally affect the level of claim settlement for the individuals insured ... However, when setting the across-the-board price of policies, such matters as costs paid out and costs recovered do have to be taken into account."
A spokeswoman for Europ Assistance adds: "E111s are reciprocal so that insurance companies can claim back the medical costs from each country. The reason we do that is to provide cover cheaply.
"For example, insurance costs are higher for people travelling to the United States, not because there is much greater sickness but because there is no reciprocal agreement with the UK."
Julie Philpott, marketing director at Columbus Direct, which sells travel insurance by phone, says: "The thing people should bear in mind is that the vast majority of cover that we provide is not met by the E111. If people fall dangerously ill and have to be repatriated, for example, the cost of that will not be reclaimable under the E111 and is simply paid by us."
Ms Philpott points out that it was up to the company to determine whether it was willing to go the whole way and demand that the insured person sign the E111 waiver form on the firm's behalf.
"We leave that decision to the customer. But if they are prepared to sign the form, we are willing to ignore the excess, which we are not legally obliged to pay under the terms of our contract."
The Europ Assistance spokeswoman adds that her company operated in a similar way. "We have many policies where there is no obligation to sign the form. In this instance, the cover was through Centurion Assistance, an American Express policy which says people must do so. We are required to respect that decision."
The Department of Health says that under European subsidiarity rules, insurers had the right to ask their clients to claim. The principle was similar to that where in the event of the theft of a handbag abroad, both the travel insurer and the home contents insurance provider will agree to share the cost of replacing the stolen goods if the bag was potentially covered under both policies.
Mr Warner is unconvinced. In the face of seeing his claim being thrown out unless he put his signature on the E111 waiver form, he said he was likely to sign. But he adds: "I think this is a disgraceful state of affairs. Something should be done about it"n