We carried our infant around in a large stroller/travel system and it worked well, especially with the larger wheels and the cobblestones.

The absolute best way to travel around London with a stroller is by bus. I was skeptical all at first, but all the timetables are available on the google map search and all of the buses are accessible and have dedicated areas for strollers and wheelchairs. It was a lot easier than trying to cram into the tube!