So what has actually happened is that they have the address or number down wrong. The charge is for reconnecting at the exchange, and clearly that line already has a connection.
Happily I did get to speak to a guy called Glen, who appears to be the only person anywhere within BT who actually wants to help. He couldn't fix the problem, but he gave me lots of info on what was wrong and how/who to get it sorted.
On we go.