All of the UK’s biggest airlines and most big holiday companies are systematically breaking the law by denying timely refunds to customers for travel cancelled during the pandemic, researchers have found.

Consumer groups have warned that the sector risks permanently losing public confidence in booking travel, with Which? finding 20 of the UK’s largest operators are illegally withholding refunds that should be paid within 14 days.

Most have instead offered vouchers or credit notes, and customers have complained they have been unable to obtain refunds online or get through to make a claim on the phone.

On Monday Ryanair started telling its customers that they will have to wait until “the COVID-19 emergency has passed” if they want a refund for a cancelled flight. Initially, the Dublin-based carrier had said it would process refunds within 20 working days but soon started back-tracking.

According to the travel industry’s own estimates, up to £7bn could be owed for cancelled trips. However, industry bodies such as Iata, for airlines, and Abta, for travel firms, say firms would be bankrupted by repaying now as they are receiving no booking revenue.

Confidence in booking is likely to have plunged further since the transport secretary, Grant Shapps, said on Friday that he would not book a summer holiday now. The Foreign Office has advised against non-essential foreign travel indefinitely.

Which?, the consumer association, said 20 of the UK’s biggest biggest travel operators and airlines were breaking the law by not repaying money promptly. It has received thousands of complaints and requests for help from people struggling to secure refunds for cancelled trips, and said vouchers or credit notes could prove worthless if firms collapsed.

However, it backed travel industry calls for the government to intervene, recognising that firms were under “unprecedented strain” and could go out of business should they process refunds immediately.

While Which? said consumers’ legal right to cash refunds should be protected, it recommended extending the processing deadline to 28 days, and for any vouchers to be guaranteed against insolvency and eventually redeemable for cash. It also called for a definitive timescale for Foreign Office travel warnings, and transparent travel insurance terms and conditions, to help restore confidence.

Which? researchers found 10 of the UK’s biggest holiday companies, including Love Holidays and Tui, are not offering full refunds within the legal limit of 14 days, with some only offering customers the choice of rebooking or a voucher. Some are withholding the air ticket price until received from the carrier.

It also found almost all airlines are failing to refund passengers on time, with many customers unable to reach call centres to process complaints.

Some carriers, such as Air France and KLM, have refused to offer refunds before a 12-month period has elapsed, issuing credit notes or allowing rebooking instead. Which? said it was “a fair solution and a reasonable balance between the protection of their passengers and the operational realities that every airline has to face”.

Passengers booking with carriers including easyJet, Ryanair and British Airways have told the Guardian they have been unable to obtain refunds. Ryanair has issued vouchers and told customers requesting refunds that they are in queue. BA and easyJet customers have complained that call centre numbers are not being answered.

A spokesperson for Airlines UK said: “Airlines are facing unprecedented challenges keeping vital routes open to repatriate stranded British travellers and transport critical medical supplies and PPE as part of cargo operations. Carriers are facing a far longer than usual volume of refund claims to get through and the current restrictions imposed nationally mean they are not able to bring in additional staff to deal with them. We are thankful to passengers for their continued patience.”

Rory Boland, of Which? Travel, said: “We do not want to see the industry suffer further as a result of this outbreak, but it cannot be on consumers to prop up airlines and travel firms, especially when so many will be in difficult financial situations of their own.

“The government must urgently set out how it will support travel firms and airlines to ensure they can meet their legal obligations to refund customers for cancelled travel plans, and avoid permanent damage to trust and confidence in the travel industry.”

Some governments have already amended consumer legislation to allow deferred refunds, after calls from the airline body Iata. The Iata director general, Alexandre de Juniac, said earlier this month that refunding was “almost unbearable, financially speaking”, adding that airlines were “perfectly conscious of the difficulty for the passenger … but it is a matter of survival”.

Abta said tour operators were being squeezed by refund requests for money that had been paid to suppliers, such as airlines and hotels, and not returned. Its chief executive, Mark Tanzer, said: “The UK government, despite repeated requests, has failed to recognise and respond to this reality, in stark contrast to the clear sensible actions taken by the European commission and many countries throughout Europe.

“We fully understand and sympathise with the frustration that many customers may be feeling. But if companies are forced into bankruptcy, it will not only destroy livelihoods but extend the refund delays far beyond the term of refund credit notes.”