Here you'll find all the information you could possibly need to plan and walk a National Trail. There are 16 to choose from!
The Long Distance Walkers Association
This website is a treasure trove of information for anyone interested in long distance walking (or running). Do consider joining if you've caught the bug!
The Ramblers Association
I've been a member of this organisation for many years and get lots of inspiration for walks. More importantly they work hard to ensure that our footpaths and rights of way are safeguarded.
For train enquiries and tickets:
National Rail Enquiries
Southeastern Railways (for Southeast London)
Transport for London
Helps you get around London by tube, bus, rail, etc.
Buses outside London:
I've found Stagecoach's website useful for planning walks in Hampshire (Wayfarers Walk, Three Castles Path).
For buses between Oxford and Reading (Thames Path)
For buses between Oxford and Eynsham (Thames Path)
For walking along the K & A canal between Pewsey and Bath