Great Britain is not difficult to navigate, and distances are not great. The longest single journey you can make, from the northern tip of Scotland to the south western peninsular of England , is only around 850 miles. Rail and coach networks are good, as are the motorways if you are driving yourself.
There are a number of different train operators, depending on where your journey takes you. Always ask for the best deals for your particular trip, and book in advance if you can, as that way you'll get the cheapest offers. Train travel can be quite expensive, so coaches make a more economical alternative. Most major towns and cities are linked by a reliable coach network, but be sure to reserve a seat before you travel. For local travel, busses are generally cheap and regular.
If you are travelling greater distances, then it can save time, and be fairly comparable in price, to fly within the UK.