Some more attempts.
1. An attempt to take out a credit card with M&S in ladysolly's name. That's been squashed.
2. An attempt to get a debit card with Santander. That's been intercepted. But I'm thinking that this means that an account has been opened with Santander using my name, so I'll have to call them and find out what's what.
3. An attempt to do online banking with Santander. Also intercepted.
I do find it quite surprising that the banks are so eager to open accounts and send out credit cards, that they'll accept commonly available information (a name, a phone number and an address) as sufficient to issue accounts.
Or maybe I shouldn't find it so surprising. In all my dealings with banks, they've shown a woeful lack of security sense.