For London to Brussels, definitely take the Eurostar. From Brussels to Amsterdam, you have the Thalys or the cheaper intercity train. You should probably fly to Prague unless you have a lot of time to take the train. Prague to Venice is probably also a flight, which would incur a connection likely at FRA or MUC. Personally I rented a car once on that trip and explored the countryside which was wonderful. Venice to Paris can be done by train with a single transfer at Milan, which you could also spend a half-day at. There are both day and night trains between Milan and Paris. And Paris to Barcelona can be done by TGV but it's a long trip doing a loop east through Lyon before heading south and stopping a multiple cities. I did Lyon-Barcelona round trip by train once and it was nothing to write home about. So I'd probably fly to Barcelona. Even driving Paris to Barcelona is boring if you take the autoroute.