In short, no.
What your son will have to do is to ask for a hearing at the fines enforcement court. Here the Magistrates will enquire into his means (or lack thereof). They will ask if he is entitled to benefits and if so why he is not claiming them. They may give him an opportunity to do so if he is so entitled. They will enquire about his current circumstances. If he is living off his mother they will enquire into that (e.g. does he get "pocket money").
At the end of their enquiries they will decide if he has exhibited "Wilful refusal to pay" (self explanatory) or whether he has exercised "Culpable neglect" (i.e. he had funds but decided to spend them somehow else). Or they may decide he has not got the ability to pay and "remit" (i.e. write off) some or all of the sums owed.
If they do decide he has had funds, however, they will make a payment order of, say £x per week (minimum, as has been mentioned, £5), backed up by a suspended prison sentence, the length of which will be dtermined by the amount he owes. The sentence will be activated if the payment order is not kept.
If he does nothing and the bailiffs are unable to secure the debt he will be summonsed to court to undergo the hearing I outlined above. If he fails to attend he will be arrested and brought to court in custody.
Unfortunately "learning his lesson" includes complying with the court orders when he was sentenced, or at least explaining to the court why he has been unable to do so. Transferring the fines to you will not see that part of the lesson learned.