Basically, the driver must be covered and the keeper must be covered for the specific car.
These are actually available to some extent. However, they are expensive and often limited to motor traders. It is this sector of the market where the new rules will impinge most, as it will presumably now be a requirement to register each car on the computer.
These are certainly available, although you may need to find a specialist insurer for anything much bigger than a city car, if you want any driver from 17, rather than 30 or 25.
Christian.