I use Lloyds TSB, with no probs
With Natwest i can access my savings account, credit card account and current account under 1 log in which means i can move money across each instantly. They also provide a card reader so that you can only send money with the unique code it provides which adds that extra security to it.
+1 for Barclays and Barclaycard. Never had any issues. Quickly sorted me out whenever I've had any issues or queries.
Halifax is one login for all accounts, you have a normal password and another where it only asks you for certain characters. If you send money to another account it asks for the password again. Seems decent security to me, also never had a problem getting any stolen money back as well, usually back in my account by the time i get of the phone.
Stolen money will always happen but for me its always been certain online shops never through the bank.
Halifax online is crap, lloyds is a little better.