Jimmy A service is not a legal obligation for a vehicle owner. It is something that is highly recommended, but it is not something that is absolutely necessary. Whilst it is recommended that you have you care serviced for your safety and comfort, it is in no way something that you have to do.
How important is it to have a full service history? It is important for your safety whilst you own the car because a service will point out issues that an MOT wouldn’t pick up. For example, it may alert you to the fact that you need an oil change.
You should also check your obligations if you have purchased your car on a PCP finance deal. You will not own the car at the end of the contract so if you are going to give it back, they may require you to have a full-service history, and you might even have to go to an approved garage.