He could be jointly & severally liable for the bills for any period when he was lving there. They could chase him for those whether his name was on the bill or not, unless their charges scheme made it clear that only the person named on the bill was liable.
His problem is proving when he moved out. Presumably he didn't tell them at the time but did tell them when the first bill arrived 4/5 years ago. Therefore if any of the bills they are chasing relate to periods after 4/5 years ago he should not have any problem getting them to accept he is not liable for those (unless they didn't keep a proper record of what he told them!).
If he has solicitors letters from ealry 2005 addressed to him at an address other then the ex-marital home then a copy of those should convince them that nothing after the date of the earliest letter is his responsibility.
Both his mother & you could do statutory declarations confirming the dates he was living with you. These should satisfy them about the date he moved out. You will need someone with some legal knowledge to draft them & they have to be signed before a solicitor who is a commissioner for oaths & witnessed by him/her.
If they still don't accept it just refuse to pay & let them take him to Court, where all the evidence can be decided by a judge.
Whatever he does, send it to them by recorded delivery & keep a copy - don't do it on the phone.