Why were they banned? They're used in the Netherlands which is rife with small bendy streets so if that was the argument it seems to be somewhat spurious.
They also cause problems for other road users such as cyclists.
Bendy buses work well if your city has wide straight roads. London's roads are neither.
the trolleys were basically replacements for trams, which needed a lot of street furniture in the form of rails, points, etc. which caused problems for the increasing use of cars. but i always liked them (trolleys).
I didn't know until now that they're only common in Britain. I guess when travelling you don't notice things like "there aren't many double decker buses".
In addition to the other reply's issues, they replaced the dirty and stinking but British-made old Routemaster buses, they were much more accessible to the disabled and babies (pushchairs), they were used successfully elsewhere in Europe, and they use more road space which could otherwise contain an important person's car.
I think they're still used in cities outside London, but that's OK since Daily Telegraph journalists never go there.