The Thames has a towpath from central London all the way to Reading, Oxford and beyond. The route is permissive for cyclists from London as far as Windsor, and passable with care as far as Oxford. Best to check if this has changed. Note that you should dismount, and walk past locks.
This route meets the Grand Union Canal (for Birmingham) at Brentford, the Wey Navigation (for Guildford and the South Coast) at Weybridge and the Kennet and Avon Canal (for Bath and Bristol) at Reading.