Traveling by train is a very good alternative to cars. Trains run fairly frequently and cover most places within the United Kingdom. Contrary to popular belief the trains do often run on time. Acquiring train tickets is just a matter of turning up at the train station and buying your ticket. Booking in advance is also a good idea especially if you are traveling from a smaller train station. If you wish to see a lot of the United Kingdom buying a week pass or longer might be worth looking into.
Buying tickets in advance can save you quite a lot of money as well as traveling during off peak times. Trains can be a lot more scenic than traveling by car or bus and have the added advantage that you keep yourself occupied whilst you are traveling.