There are lots of websites nowadays that will give you walking directions between two points. Here are just some of them:

Multimap

Put your starting point in box ‘A’, where you want to go in box ‘B’ then check the ‘walking’ box and you’ll soon be on your way.

TfL Journey Planner

Transport for London’s Journey Planner also has walking options. Use the above link to select the Walking Journey Planner. If you aren’t interested in using any other modes of transport on your journey, make sure you deselect those boxes. This link also has lists of strategic walking routes in London. TfL also has a host of other tools to help you get around.

Walkit.com

Covering 29 UK cities, and more being added all the time, this site helps you plan a route map between any two points, including info on journey time, calorie burn, step count and carbon saving. Now also includes circular route planning - perfect for lunchtime walks.

Google

Google provides walking directions through its map site. To access the walking directions, go to 'Get Directions,' put in your start and finish points, and select 'Walking.' Please note that this feature is still in Beta (testing phase) and may be missing pedestrian pathways.

Transportdirect.info

Transport Direct is a non-profit service funded by the UK Department for Transport, the Welsh Assembly Government and the Scottish Government. It offers information for door-to-door travel for both public transport and car journeys around Britain. This site can be useful for planning long journeys where you can combine public transport with walking.