Thanks to everyone who commented on this.

Looks as if the scam works like this for the perpetrator:

- Choose an address not too near home
- Start the process of opening an online bank account at that address. This will give a valid bank account number
- Use the bank account number to set up a direct debit mobile phone contract. The free handset will be delivered to the address of choice using next-day delivery
- (the difficult bit) either explain to the person who lives at the chosen address that the parcel will being delivered in error and ask them to sign for it, or hang around and intercept the courrier
- Get as much use as possible out of the mobile until the whole thing folds up, which happens quite soon. The phone company notices heavy usage and closes the contract, or a phone bill or a letter about the new bank account arrives at the chosen address and causes suspicion. Banks and mobile phone companies know about this kind of activity and are happy to close accounts immediately.
- When the phone is made unusable, sell it on.

It hasn't been much fun being on the other end of one of these scams, but I'm thankful it is nothing worse. Or maybe it is something worse but I haven't found out yet!!

Jane