Can someone who is not a named driver on my insurance supervise me, the learner?

If you are going to be learning to drive in a private car (that is not in an approved driving instructor's car), then you will need to be insured on that particular car. Once your insurance is sorted, you can start your driving practice as long as you're supervised by someone who is over 21 and who's held his full driving licence for a minimum of 3 years. The supervisor does not need to be insured on your car or have any car insurance in his name but he needs to satisfy the conditions stated above and you must always be accompanied at all times as long as you hold a provisional driving licence.