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Thanks for your question.
The only cooling off period implied in to consumer contracts (as this one is if you were not buying as a business) is by the Consumer Protection (Distance Selling) Regulations 2000. Unfortunately for this to apply you must have been sold the car over either the internet, digital television, mail order, phone or fax. Obviously this is not the case here so the 7 day cooling off period is not implied in to your contract.
You will only have a cooling off period if it has been expressly stated in to your contract or possibly if the dealer orally agreed to one over before you put down the deposit so I'm afaid you're on shaky ground here.
Sorry it could not be better news. Good luck with the dealer, hopefully you'll be able to be able to negotiate some kind of compromise (although they are under no obligation to do so.
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