Can you please confirm whether this was purchased from a dealer or whether it was purchased from a private seller?
The rights and remedies are different
If somebody does work for someone else, provides a service, or supplies goods, and does so as a business to a consumer, then under the Consumer Rights Act 2015 the:
Goods must be as described
Of satisfactory quality
Fit for purpose
And any service must be as described and carried out with reasonable care and skill.
If no price is specified then the price must be “reasonable” and if no timescale is specified the timescale must be “reasonable”
If on the other hand goods are being sold by a private individual to a private individual, they only have to be as described.
In the case of a vehicle it also must be roadworthy otherwise it’s a breach of section 75 of the Road Traffic act.
So if it was a private seller and they didn’t mention anything against the keys, then you are stuck with it.
If on the other hand it was from a dealer it substantially not of satisfactory quality and you would be entitled to return it and get your money back.
Don’t get excited, car dealers won’t do that and you would end up taking them to court although very often they will settle before court proceedings.