My understanding is that a charge in and of itself does not force a sale - rather that when the house is eventually sold, for whatever reason, the charge applies and the required amount of money must be handed over out of any equity.(posted 7871 days ago)Your friend & his partner really do need legal advice on this, and proper financial advice about taking out a second mortgage to attempt to pay off the charge, and so the Citizens' Advice Bureau, a legal centre or an access point is the next obvious point of call.
By the way, driving uninsured is a serious offence so presumably your friend was prosecuted for this and received some legal representation and advice at the time? Perhaps it might make sense to consult the same solicitor who knows the case to ask for further advice. Just a thought.