I've been using this since I moved over here, and don't think anyone else has linked to it. Since there seems to be an influx of new UK residents, thought it might help people out.
Transport Direct's Journey Planner
It allows you to pop in where you are and where you're going and it give you a few route options, by car or by public transit.
Even knowing my way around here, I used it today to get an estimate of how long it would take me to walk from one bus stop to where I had an appointment, and to see what bus line ran there in case it started raining.