We have had a number of cases go to court recently on this point, and the law is clear.
Under the Consumer Rights Act 2015, if a consumer agrees to a repair, they cannot simply change their mind and ask for a refund. This applies both within the 30 Day Right To Reject period and beyond. A trader’s obligation once a consumer has indicated that they will accept a repair is simply to:
(a) complete that repair within a reasonable time and without significant inconvenience to the consumer, and
(b) bear any necessary costs incurred in doing so.
Of course a “reasonable” time is subjective but generally speaking if a dealer takes couple of days to repair as opposed to a couple of months, then this would be reasonable. Further, dealers should note that you can cause some inconvenience to a customer. However, significant inconvenience is not allowed. Again this is subjective. However, in most cases if a dealer orders a part and gets it fitted without leaving the vehicle languishing around in storage for weeks on end, this shouldn’t cause any issues or allow the customer to reject.

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