I am passing on the following story verbatim because it happened to a friend who is particularly aware of the risks and still got caught.
If your mobile phone suddenly stops working with the error "Sim registration failure" or similar and it is the number associated with your internet banking account check what's happening on your bank account. My mobile was barred last Friday at 10:44 am after someone phoned Vodafone to report it missing. By 11:09 some lowlife ba$tard had extracted almost £3k from my current account. (it was an unusually high balance due to having imminent bills for a boiler and some double glazing) It appears that said lowlife reports your mobile stolen, hoping to get calls diverted to a number of their choice in case the bank rings about the unusual transaction activity on your account. Luckily Vodafone will only apply a divert if the caller can prove they are the mobile account holder. In this case, Halifax spotted the unusual account activity by the 4th transaction and locked the bank account. They then assured me that the missing money will be replaced by tomorrow now that I have scanned my IT equipment for nasties and the account has been re-activated with new security information. So, the moral of the story is, don't be complacent when your phone stops working - I was originally going to wait until I could get to a Voda-shop to get the SIM checked but after not being able to access my bank account, I rang them to sort the phone out and discovered the link.
As they used to say on Crimewatch -
Be careful but don't have nightmares.