Taking the decision to travel to Europe by rail, rather then flying, really depends on where you live in the UK and where your destination is. If you want to travel from the south of England to northern France, Holland or Belgium, it may be quicker and less hassle to take Eurostar from Waterloo, London. You can just arrive a few minutes before the train is due to depart, no getting to the airport to check in hours before your flight. You can arrive directly in the city centre of your destination, with no waiting for luggage at the airport. It could also be cheaper, you don't have to pay Air Passenger Duty etc. and it is a much greener way to travel than all the CO2 emission caused by flying.
For rail travel within the UK, East Coast trains go to some great destinations for international travellers, including Edinburgh York, Durham and London. I use East Coast trains quite often, as I live in Berwick upon Tweed, in between Edinburgh and Newcastle upon Tyne. You can usually find the cheapest train tickets if you book at least a couple of months in advance of travel. Often two single tickets are cheaper than a return.