Main national rail routes are served by a variety of private train-operating companies. Tickets are not cheap, but trains between cities are usually quite punctual. Check National Rail (www.nationalrail.co.uk) for timetables and fares.
Eurostar (www.eurostar.com) High-speed passenger rail service linking London St Pancras International with Paris, Brussels and Lille, with up to 19 daily departures. Fares vary greatly, from £29 for a one-way standard-class ticket to around £245 each way for a fully flexible business premier ticket (prices based on return journeys). New direct links between London and Amsterdam and Rotterdam commenced in 2018. There are deals on Eurostar Snap (available on Facebook), with best-value fares for those with flexibility around the specific train they travel on.