Still not quite right given what we're discussing. A standard road going car needs to be insured by someone, but someone who isn't insured for it can still drive it on private property.It most cases this is correct.
S144A(1) requires a motor vehicle registered under the Motor Vehicles Excise and Registration Act 1994.
If the motor vehicle is registered under the Act (is it has a licence plate) then to be exempt from insurance requirements it must have SORN in place. There are a number if other exemptions for Army vehicles etc which are not relevant.