Wayfair is among three firms which have been fined £6m in total by the competition watchdog for illegally using misleading sales tactics – with some customers set to receive refunds.

The online furniture retailer was fined £4.8m for misleading customers with time-limited offers, while online electronics seller Appliances Direct was fined £1.2m for the same practice, the Competition Markets Authority (CMA) said.

Meanwhile, Gold's Gym has been fined £45,000 for not telling customers the total price of its memberships.

It and Appliances Direct have been ordered to refund customers a total of £440,000. Wayfair and Appliances Direct said the CMA's fines were disproportionate.

Thousands of Appliances Direct customers will receive refunds of £25 each on average while 726 Gold's Gym customers will get refunds of up to £50, according to the CMA.

The watchdog said customers do not need to take any action and both companies will contact those affected customers about refunds.

Appliances Direct has been told to pay refunds by 11 March, while Gold's Gym has been given a deadline of 29 March.

The CMA said Wayfair, Appliances Direct, and Gold's Gym had "engaged constructively" with its investigation. They all admitted to breaking the law and agreed to settle the case early, it added.

The watchdog said their co-operation reduced the firms' fines by 40%.

The CMA's fines are the result of an investigation it launched last November into online pricing.

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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.