As noted above, many motoring offences do not require intent. They are offences of strict liability.
Regardless of the currency of an MoT certificate, it is an offence to drive a car which is not roadworthy (because it has some safety critical defect). For example, a car that passed an MoT test last week is unroadworthy if since then its brakes have failed, or an accident has rendered the car structurally unsound. If a car is roadworthy then, as mentioned above, it may be driven any distance to a pre-booked MoT test.
If your car is taxed it must also be insured. To store a car untaxed and uninsured off road you make a declaration online that the car is off road (SORN).
If driving a car that is not yours, or letting someone else drive your car, check that you or the other person (as the case may be) is insured to drive the car. Allowing someone to drive your car when that person is not insured to do so is an offence. Most comprehensive insurance policies cover you to drive a car that is not yours with the owner's permission, although usually the cover is limited to liability to third parties.
Once a vehicle is forty years old, it does not have to pass an MoT test (this is a daft idea), and (more sensibly) it can become exempt from tax and the ULEZ charge (but not the London Congestion Charge). For the young driver who has some mechanical sympathy and doesn't mind doing repairs or paying for repairs, driving a classic car or riding a classic motorbike can make more financial sense than you might suppose. What you may lack in air bags you can make up for in fun, eco sustainability, and ability to see out of the car, and an old car can be fitted with a modern ICE unit which includes satnav, a reversing camera, and so on.