Virgin Experience Days shoppers are being urged to check whether they were signed up to a paid membership without realising.
MoneySavingExpert said its team found the £9.99-a-year Memory Makers+ subscription was being added to orders through a pre-ticked box at checkout.
The consumer website said it spotted the issue when it visited the company's website on October 30 and reported it to the Competition and Markets Authority (CMA).
MoneySavingExpert said Virgin Experience Days changed its website after the issue was raised, so the membership box was no longer selected by default.
The membership offers discounts on purchases, free greeting cards and other benefits, and renews automatically each year.
CMA guidance says businesses must obtain a customer's express consent before charging for optional extras.
It says a pre-ticked box does not provide that consent when a customer must take action to avoid an extra charge.
The regulator also says customers who did not expressly agree to an additional charge are legally entitled to claim a refund.
How to check for a membership
MoneySavingExpert recommends searching email inboxes, including junk and spam folders, for an account activation message to check whether the membership was added.
It advises customers who want to cancel or request a refund to contact memorymakers@virginexperiencedays.co.uk.
A Virgin Experience Days spokesperson said: "Memory Makers+ remains a relatively new addition to our business, and we continually review and refine the programme based on performance data, customer feedback and regulatory developments."
The company said most customers saved more than the cost of membership on their first purchase and that it received positive feedback about the scheme.
The spokesperson added: "In the small number of cases where a customer wishes to cancel, we operate a seven day a week support operation where queries are handled within 24 hours."
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