Well it seems that you have committed two motoring offences - driving without insurance and learning to drive under the supervision of an unqualified driver. For someone to be able to supervise a learner driver like yourself, the person must be at least 21 years old and have held their driving licence for at least 3 years. For this offence alone, both you and the person who supervised you can expect to pay upto £1000 in fines, get 3-6 points on your licences and may as well receive a driving ban. Not having a valid insurance policy whist driving can result in an instant ban, with a fine of upto £5000 and 6-8 endorsement points on the licence.
The information above is the maximum punishment you would get for each individual motoring offence. However, the penalty is usually less and do not constitute the sum of all punishments. It is worth noting that if your licence is endorsed with 6 points during the court's hearing and you pass your driving test in a few weeks time, then even getting one additional penalty point on your licence will result in the revokation of your licence and you will have to do it all over again.