O2's 3G network is very slow....
T-Mobile's is the best 3G/HSDPA network BUT if you get the SOLO which is the equivalent of the O2 Simplicity plan mentioned above you get 600 mins unlimited texts and internet access (capped at 1Gb.month) but it is 3G only - you will not get HSDPA so will be limited to 384kbs
O2's 3G is HSDPA enabled but when I tried it the speeds were appalling, varying between zero and 500kbs.
On T-Mobile contract my speed varies between 1100 - 1900 kbs.
If you are staying in London you should get coverage on all networks but Three are truly appalling, Orange data is slow and expensive and voda have a good network but not good price plans.
The T-Mobile Solo and O2 Simplicity plans are monthly contracts - you pay your £20 and get your allowance for 30 days, if you don't pay the following month I believe (but am not certain) that they revert to standard PAYG - on T-Mobile internet usage is capped at £1/day or you can get a 5 day pass for £2.50.
I would suggest the £20 Solo from T-Mob or the same Simplicity plan from O2 if you really don't want T-Mob either should be suitable and both do more expensive plans for more minutes and texts but the cheaper plans (£15/month) don't include internet on either so avoid them.
Pay Monthly Sim Cards - Mobile Phone SIM Cards - T Mobile