Yes, it is legal to wrap your car, there are currently no laws in place, however, there are restrictions to what you can do for example impersonating a UK police car.
When you have your car wrapped even though it is not a permanent change it is important to inform the DVLA of the change. As the registered owner of your vehicle, it is your responsibility to inform the DVLA, to update your vehicle's CV5 certificate you can do this by clicking here. If you need any help a member of the team is always available to help.
Additionally, you should notify your insurance company that you have had your vehicle wrapped or parts of it. Although the cost of your insurance is unlikely to change because of it, the company will want to be aware of any costs in regards to fixing or replacing the wrap – should you be involved in an accident.