There are several routes you could use, which will take between 21.5 and 25.5 hours. 1. Eurostar from London to Lille (1h20m); TGV from Lille to Perpignan (6h48m); local train Perpignan to Port Bou (Spanish border) (53m); local train Port Bou to Barcelona (2h23m); overnight in Barcelona (7h50m); EuroMed Barcelona to Alicante (4h40m). 2. Eurostar from London to Paris Nord (2h22m); cross Paris by Metro; TGV from Paris Montparnasse to Irun (Spanish border) (5h38m); local train Irun to Valladolid (5h18m); hotel train Valladolid to Madrid Chamartin (3h05m); Talgo from Madrid to Alicante (3h45m). 3. Eurostar from London to Paris Nord (2h27m); cross Paris by Metro; Euronight sleeper from Paris Austerlitz to Barcelona Estacion de Franca (9h52m); metro from Barcelona EdF to Barcelona Sants.; EuroMed from Barcelona Sants to Alicante (4h). www.seat61.com is a great site for advice on train travel in Europe (and elsewhere round the world). Most of the trains mentioned will involve special fares, s