Recreational cycling in London

Do you mean to take a bike on the underground to further out of London? You might struggle with that as they don't allow bikes on a lot of the lines. I think you can do it on the overground from canada water, best to check tho. I had to strip a bike down to parts one time at Old Street, right there in the entrance to the station. I'd just bought it as a resto and wasn't rideable. WHat a fookin nightmare. >:(
Map of where bikes are allowed on London Underground [pdf]