Hi,
it's very possible that National Grid Transco etc have your father's MPAN or Meter Serial Number associated with a different address. This means that if someone at that other address applies for a different supply, British Gas would think your father is leaving.
Contact Consumer Focus (Formerly Energywatch, they may still be listed as this). They will take the complaint forward for you to BG and hopefully get to the bottom of it. Of course you'll need your father present when you make contact so he can give his consent for you to deal with the complaint.
As for moving supply, it's incredibly easy these days, and you may well find that your father can get a better deal elsewhere. As i said earlier, as long as your father is present to give consent during the phone call, you are allowed to change suppliers for him.