The question here is what is the difference in value between a car with full service history, and a car with no service history.
Useful information in determining that would be the age of the car, the mileage on the car when bought, if you bought the car retail (from a trader) or privately, if you have evidence that the car was advertised as having FSH.
Basically, you find out that difference in value, and write to them (recorded delivery), informing them that if they don't provide you with the service book OR the difference in value, then you will take them to Trading Standards / small claims court.
They will then either pay, ignore you (in the hope that you are bluffing), supply the book, or make a counter-offer.
You will then have to decide just how far you want to take the matter.
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