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As above, anywhere worrth browsing around to kill a couple of hours this afternoon?
Swift cycles is good and enthusiastic bunch, not a huge amount to see:
http://www.swiftcycles.co.uk/pages/about
There is a cyclesurgery close, and there is another and an evans near Liverpool Street
Bobbins for that type of stuff...
http://www.bobbinbikes.co.uk/wordpress/
Bikefix for recumbents and cargo bikes:
http://www.bikefix.co.uk/shop/
On your bike near London Bridge, and an Evans close by:
Lookmumnohands. Pretentious and ****y, but they do nice coffee and cakes. 🙂
http://www.lookmumnohands.com/
Condor should be paid a visit too. Brick Lane bikes for fixie-hipsterness.
Condor are on Grays Inn road.
Brick Lane Bikes worth a look for vintage bikes and fakenger chic, but predictably plagued by Nathan Barley types.
Bit out of the way but Brixton Cycles is worth a visit.
EDIT Toby Mc beat me to it!
the Cyclesurgery at Spitalfields (not the one in the market, the other one) is MTB-specific and worth a browse if you're near Liverpool Street.
And as much as I hate to admit it, the Evans in Spitalfields Market is pretty good and has a big big room downstairs with loads of stuff in.
Condor is a nice roadie-oriented shop with lots of bits to look at and clothes.
On Your Bike at London Bridge is big and browseable.
Problem nowadays is that most of the London bikes shops cater for commuters so are full of hybrids, faux fixies and every possible item of clothing available in hi-viz yellow.
EDIT: I really want to go to Brick Lane Bikes but the people in there make me fell all punchy.