The V5C is the registration document for a vehicle. People call it the logbook and assume it is a certificate of ownership. It is not. The V5C says, on its own face, that it is not proof of ownership. It is a record of who the registered keeper is, which is a different thing entirely.
When you register a vehicle with the DVLA, you transfer it from your private ownership into a registered status. The DVLA becomes the keeper of the record. You become the registered keeper. The vehicle, as a registered article, falls under the statutes that govern road traffic, vehicle excise, MOT, and insurance. None of those statutes apply to private property used privately. They apply to registered vehicles used on the public road.
The lawful position
A living man or woman has the right to travel and the right to own property, including a means of conveyance. That right does not depend on registration. What registration does is convert a private conveyance into a regulated one for the purposes of statute. It is a contract of registration, offered by the state, accepted by the act of submitting the V5C and paying the fee.
You can, lawfully, withdraw from that contract. You can return the V5C with a notice stating that you no longer consent to be bound by the Vehicle Excise and Registration Act in respect of this property, and that the conveyance reverts to your private ownership. From that point you do not pay vehicle excise duty, do not require an MOT, and do not require road insurance, because none of those statutes apply to private property used privately.
Hold the line
This is the area where the gap between lawful position and practical enforcement is widest. ANPR cameras, constables, insurance databases, and your own neighbours all operate on the assumption that any vehicle on the road must be registered, taxed, MOT'd and insured. A constable who stops you will not be persuaded by your lawful position at the roadside. A magistrate who hears the case will, in most cases, side with the statute.
Practical sequencing matters. Do not test this position by driving an unregistered, untaxed, uninsured vehicle into central London. If you choose to step out of the registration scheme, do so in a way that minimises confrontation. Use the vehicle on private land, on quiet rural roads at sensible speeds, or for limited journeys where a stop is unlikely. Carry your paperwork. Know your scripts. Accept that this is one of the costliest areas to test, and decide carefully whether the lawful position is worth the practical exposure for you, today.