Complaints over refunds for childcare, holidays and weddings are being investigated by the competition watchdog.
The Competition and Markets Authority (CMA) said complaints around cancellations and refunds account for four in five of those received by its coronavirus taskforce.
Concerns include businesses refusing refunds or firms pressuring people to accept vouchers for holiday accommodation, which can only be used during a more expensive period.
The watchdog said consumer rights cannot be ignored.
Businesses should also not be profiting by “double recovering” their money from the government and customers, the CMA added.
If it finds evidence that companies are failing to comply with the law, the CMA will take enforcement action, including moving quickly to court if a firm does not address its concerns.
Customers can also take their own legal action against unfair terms.
The CMA said it has identified three sectors of particular concern – weddings and private events, holiday accommodation, and nurseries and childcare providers.
It will tackle these areas as a priority and then move on to other sectors, based on the information received by the taskforce.
However, it added that most businesses are acting reasonably in what are unprecedented circumstances, and the crisis is placing everyone under pressure.
The CMA also outlined its views on consumer protection law in relation to cancellations and refunds during the crisis.
Andrea Coscelli, chief executive of the CMA, said: “Our Covid-19 taskforce is shining a light on some of the big issues facing consumers in the wake of this pandemic. Alongside price-gouging reports, we’re now seeing cancellation issues in their thousands.
“The current situation is throwing up challenges for everyone, including businesses, but that does not mean that consumer rights can fall by the wayside. If we find evidence that businesses are failing to comply with consumer protection law then we will get tough – that means launching enforcement cases and moving to court action where there is a strong reason to do so.”
If people have been affected by unfair cancellation terms, they can report them to the CMA using an online form at coronavirus-business-complaint.service.gov.uk.
While the CMA cannot respond directly to every complaint, the information provided will help decide which issues to address as part of its work.
Adam French, a consumer rights expert at Which?, said: “We’ve heard from many distressed people who risk being left out of pocket for significant sums of money as they struggle to get refunds for cancelled weddings, private events or holiday accommodation.
“It’s right the CMA investigates sectors that are skirting their legal responsibilities on refunds and cancellations by trying to rely on unfair and unenforceable terms and conditions.
“The regulator must be prepared to step in and take strong action against any businesses found to be breaching consumer law and taking advantage of consumers during these unprecedented times.”