Trains

The UK has an extensive rail system allbeit rather expensive with trains often running late.  That aside it's possible to visit the majority of mainland Britain via train and it's still far faster than road transport.

A new visitor to the country is more than likely going to arrive at one of the major airports.  All London Airports have train stations as does Manchester and a few other regional airports.  Other airports usually have a bus link to take you to the nearest station.

Those visiting from mainland Europe may consider taking the Eurostar service via the channel tunnel.  Trains depart from Paris and Brussels and currently terminate at London Waterloo.
The following link is to the national railway enquiry line. It has loads of inforamtion like timetables, fares and maps.