Each borough in London does it's own thing. Some are good, some are not so good, others are somewhere in between. It seems London puts a lot of its routes down backstreets, and is pretty good at doing salmon-run lanes and not having ridiculous right-angles and gates everywhere like Edinburgh loves. It's a real mix though.
I've cycle a lot in Central and North London, but generally had a guide. It's worth planning where you're going with some care to avoid bad and big roads. It's generally quite easy to avoid the worst places, although some junctions (Kings Cross, Bow etc.) it's very difficult to get around without a big detour.
London a bit odd as drivers do seem more aware of cyclists (probably due to the sheer volume) however levels of aggression are higher, and London buses are best steered clear of entirely on the roads. There's a lot more HGVs in London, generally rigid-framed tippers, I assume from the sheer amount of building work always going on.
I prefer the bike to the underground. It's definitely good if you want to get out of the centre a bit. There are some nice routes along the Thames up river a bit that will take you to Richmond. Bike will take you interesting places that public transport wont. The tube is terrible for spotting cafés from, and the view from the carriage is rubbish!