Update time, if anyone gives a toss!
I just spoke to my Auntie, and she said the odds are very good that it's a scam. It's pretty common, and this is how it works:
Someone will find my name and address, then go into a bank and say that they want to pay some money into my account. They don't have the account number to hand but they have my name and address. So the cashier will look that up, and if they find an account, they'll pay the money in. Of course, they will get a receipt, which just happens to have the account number on it. Voila, part one complete!
They'll then pay some small amounts into the account, and log the dates/amounts/locations. Then they'll make their move. One day they'll go into a branch to withdraw some cash. The cashier will ask if they've got any ID on them, to which they'll say that they haven't, but they can tell them that they paid x amount into the account here/here/here and here, and bingo, the cashier will let them have what they want!
She told me that she knows the manager of my local branch of Abbey National, and she's a bit of a d1cksplat, and that I need to go in there and tell her how to do her job, and what to do
Meanwhile she's going to open an account for me with her bank, so I can shift all my money