A Wayfair spokeswoman said the penalty was “excessive” but that “we take the CMA’s findings seriously and we chose to settle so we can continue to focus on serving our customers”.

Nick Glynne, chief executive of Buy it Direct, which owns Appliances Direct and several other online retailers, accepted that its practices were wrong, but said the firm should have simply been given “a rap on the knuckles” instead.

Glynne said the CMA’s process for calculating the fine was a “black box” and that it only settled because appealing was too expensive, accusing the watchdog of pressure tactics.

“When one body is investigator, prosecutor, judge and jury, it needs an exceptional commitment to fairness, restraint and proportionality. That is not what we experienced,” he added.

Hayley Fletcher, senior director for consumer protection at the CMA, said: “At a time when many households are carefully managing their budgets, people shouldn’t lose out because of misleading sales tactics.

“Businesses must treat their customers fairly and make sure they comply with the law – or risk hefty fines.”

Sue Davies, head of consumer rights policy at Which?, praised the CMA’s response.

“The refunds secured by the CMA are a much-needed win for consumers at a time when household budgets are under strain,” she said.

The CMA’s investigation found that the three companies had misled customers in different ways.

Wayfair had advertised products as if they would disappear the next day, through phrases like “Here Today, Gone Tomorrow” and countdown timers.

However, the CMA said many products remained available at the same price or lower after the stated deadline, meaning the time-limited offer was false.

Meanwhile, the regulator said Appliances Direct had automatically opted customers into services such as recycling old machines.

Gold’s Gym was fined for failing to include joining fees in the total price of gym memberships or not making its total price clear to customers, the CMA said.