Bradford & bingley are not affiliated to any other bank or building society, however if you are looking for best savings accounts try Kaupthing edge at 6.55% & guarantees to be 0.30% above bank of england base rate until Feb 2012(make sure its kaupthing edge as there is a kaupthing) whose account is covered by FSCS or Birmingham Midshires 6.52% also covered by FSCS - both are easy access so no penalties should you need to make a withdrawl & online, also the B&B account is good & FSCS covered.
Kaupthing edge also has a 7.15% 1 year bond which is interesting.
If you have cash ISA's Principality has a 6% rate for transferring in previous years & Barclays has one of the better rates for news ISA's at 6.25% but make sure you move it after 1 year as the rate plummets to 4.85% ish.
I have recently opened accounts with all the above without problems.
Hope this helps,
Burger