This is really only a question you can answer for yourself.
How fit are you? How much do you ride currently, is 11 miles a long way for you? Are you comfortable in London traffic? Is it raining?
These questions, and others, you will need to answer before you get close to an answer. Personally, I'd do it, I chose 2 points on the map in London at random and it shows about an hour by bike, an hour by car and 30 mins by train.
As for clothes, you may find that your office has a shower or changing room and you can change from something in lycra to something more office friendly when you arrive. Failing that, a lot of people recommend baby wipes. There's other questions about commuting with a lot of information on this.