hugoboss..." They claim it is a 12 month contract - we pay monthly though."
The are not 'claiming' anything - their terms and conditions state you are signing up for twelve months (I used to be with them for a short while).
It is commomplace to sign up for a 12 month contract and pay it monthly, and upon your first dial in you accepted this and started your 12 months.
You don't necessarily have an automatic right not to pay because you changed phone providers - you will have to do as you said and appeal to their good nature, though, as you said you were only with them for 5 months, that isn't even half of their minimum term. Perhaps if they don't accept a complete termination of contract you could make an offer of some form of payment (i.e. their admin type costs or something for the remaining period) and close it that way.