A Trojan Virus is circulating on computers that purports to come from TESCO asking for banking details as part of TESCO’s Random Security Identification Check and asking for all your details that you would normally enter to use your account. Obviously don’t give any details of your account. Contact TESCO immediately by phone so they can remove it for you.
If you get an e-mail from any one. Do not just click on the link. I know it’s a pain but type in the URL your self.
This wasn’t an Email it was what came up on screen when my wife logged into her TESCO Account.
Why on earth/ how will Tesco “remove” the “trojan virus”. That pop-up sounds suspicious to me.
Lord only knows but that is what they said, I think they maybe ment the account as it has been removed. I cleaned by computer with SUPER AntiSpyware.
Similar thing with HSBC business banking last week.
Sorry I did not see this was your own computer has been compromised.
The only way to fight this is:
A. Use Luinx or a Mac
B. Always use the latest anti-virce/spyware/firewall software with the updates.
Its hard and my wife had her lap top done over. It takes even more work to clear these things off. 
PS thank for post.
Your bank will NEVER ask for your details. Why should they when they already have them?
It sound like your machine may have already been compromised in the past. As others have said. ALWAYS use up to date, quality antivirus & firewall software. The Norton 2010 suite is very good and not too expensive. It checks emails and web pages for viruses or payloads that may hit your machine and has a low impact on how your PC runs too.
Run a full scan with your virus checker.
If using Windows/IE, makes sure that your machine is fully patched up, or use Firefox, though that is comming under the attention of scammers.
Have you telephoned your bank directly using the phone number on your bank card or statements? DO NOT followed any links or phone numbers that were in the webpage that you had.
Check your bank for suspicious activity.