Look at the distance to work and the distance to the Dorking train line. Tooting would be quite good location. Not fare to SB and not far to get on the Dorking / London line plus not bad price wise.
Also regarding cycling in London don't be too proud to do some cycle training, you could be a cycling god off road / BMX e.t.c but cycling in heavy traffic is very different and many people do so very poorly. Modern cycle training is not like cycling proficiency. Being a good cyclist in traffic is not to do with being a master of bike control / speed just like being a good driver on the road has little to do with being a master of drifting.
"great views of the City and Thames, pretty quiet"
When was that then? When I have visited that great dump of noisey, filthy, horrible place there has been the constant drone of aircraft, sirens, and traffic in general… oh then theres the black bogies.
If you can't tell I never have fancied London, although I know plenty of people who moved their for jobs in their 20's and now in their 30's they want to get out!
Living on your own in london is very expensive when you consider all the bills as well as rent. House share is definitely the way to go. Search on moveflat or gumtree. Anywhere near a decent rail line to get out of town for riding.