While I plan my trips I use a variety of websites to do this. Below is websites I frequently use for my travels.
Real Time Trains
Possibly the most useful website for planning trips, especially trips where you are wanting to tick off stations. It's also really useful for when tracking where your train is and if it is on time.
BR Fares
When you are wanting to see what type of tickets there are on the route you want to take. Can be seem complex at first, but after a bit of time it becomes quite easy to understand.
TrainPal
My go to website for purchasing train tickets online. The split ticketing system is usually the most thorough in my experience. The more you use TrainPal the better the benefits, e.g. Paller Premium level has zero booking fees, No refund fees & cashback per booking!
Bustimes.org
When it comes to planning bus journeys this website is an absolute must use! It includes every single bus route that is in the UK. Not only that, you can track the buses for most operators in Great Britain!
Open Street Maps
While most would probably use google maps to work out their walks. I would recommend using Open Street Maps. This website shows not only the roads, but many of the public rights of ways! This website got me to Cornwall from London!