Hi Tess, the tfl website is fine for travel within the London area, but if you intend to travel elsewhere then public transport is patchy.  For inter-city travel, trains are OK but can be expensive.  Although trains are operated by different companies the website www.nationalrail.co.uk includes all of them.  Alternative intercity travel is available by coach - try www.nationalexpress.com or uk.megabus.com.  Local travel within cities is generally OK by bus or train (and in some cities, like Glasgow and Manchester, by metro or tram), but providers operate their own websites.  In the countryside, public transport is generally poor (infrequent or absent).   Good luck!