Local MP's are good to write to if you want to get BG to sit up and take notice of you - as, suddenly, it has gone from a problem with a customer to a potentially bad PR situation.
In reality though, you will get a letter back from MP's office saying "thanks for your letter" and "expect a reply usually within two weeks", but you will be quite fortunate if the follow up offers any REAL help.
It is a good window of opportunity to ask BG to substantiate their claim by billing breakdowns and a usage summary. If they provide it, you may realise you do owe the money . If they cannot, then you may successfully argue that you oew then nothing.
By the way: If your bill was from a shared household and was in your name, it doesn't matter how many were living there, the bill is down to the person who's name its in.
Good luck