Customers of the deals website Groupon who were told by the firm they had to accept a credit note could be due cash refunds after the UK’s competition watchdog ordered the company to improve the way it treats users or face legal action.

The Competition and Markets Authority (CMA) said this week it had found evidence that Groupon does not always provide customers with refunds or replacement items when there is a problem with an order. Shoppers have sometimes only been offered Groupon “credits”, potentially breaking consumer law, it says.

Groupon started out selling vouchers for experiences such as hotel teas and outdoor activities, and now sells a bewildering range of “discounted” items and services – from lawnmowers to deodorant.

The company partners with retailers and other service providers to offer items, and helped to spawn a huge voucher and deals industry. However, some customers have reported huge frustration when it comes to getting refunds or a replacement when the service or item can’t be provided as advertised or simply fails to arrive.

The CMA has told Groupon it must make “swift” changes to how it deals with customers to “ensure it is complying with consumer protection law”.

It remains to be seen whether that will include the offering of cash refunds to affected customers.

In a statement, Groupon says: “We have and will continue to cooperate fully with the CMA. We take the outcome of the investigation very seriously and will be carefully reviewing the CMA’s findings.”

Some customers such as Zai Hussien say they have struggled to get their money back. In his case, he bought a voucher for the servicing of his car’s air conditioning system. However, the garage could not honour the voucher and told him to ask for a refund. He told the website Trustpilot this month that he was only offered a credit note. In a reply posted on the site, Groupon said: “Our apologies for any issues with receiving your refund. We’re very sorry to hear about the poor experience you’ve had with us so far.” It invited him to contact customer services about the status of his refund.

In a statement, the competition watchdog says it has “found evidence that Groupon does not always provide customers with the refunds and other forms of redress, such as replacement items, to which the CMA considers they are legally entitled”. It is also concerned that Groupon was failing to ensure that vouchers people had bought could always be redeemed within the advertised periods.

The CMA has written to the company to ask it to sign formal commitments. This could include Groupon providing redress to shoppers wrongly denied a refund, although the exact action is yet to be confirmed and will be subject to discussions between Groupon and the CMA. If Groupon fails to act, it may face court action.

This is not the first time Groupon has found itself in trouble with regulators. In 2012, it agreed to change some of its business practices after an investigation by the CMA’s predecessor, the Office of Fair Trading. At the time, Groupon pledged to ensure that information on its website was not misleading and to comply with customers’ legal cancellation and refund rights.

Adam French, a consumer rights expert at Which?, says: “Which? has previously uncovered problems with misleading Groupon deals, so it’s good to see the Competition and Markets Authority taking action to tackle the company’s poor treatment of its customers. Consumers should remember that if they are struggling to get a refund and paid more than GBP100 by credit card, they can try to claim a refund under section 75 of the Consumer Credit Act or use chargeback rules if they paid on a debit card.”