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It's also possible to go via Krakow, using the daily Krakow-Lviv sleeper train, an ideal route to stop off in Krakow and see two great cities on one trip. Indeed, it's possible to go London to Prague, sleeper train Prague to Krakow, then this sleeper train from Krakow to Lviv - three of Europe's best cities in one trip!
This visa-free arrangement was introduced in 2005, but has been extended indefinitely. With the current situation in parts of Ukraine such as the Crimea, check Foreign Office travel advice at uk/foreign-travel-advice.
If you prefer daytime trains and hotels to sleepers, and fancy a morning (or more) in Krakow on the way, this is ideal.
If Krakow has become the new Prague, then Lviv is the new Krakow...
Treat yourself to a meal and kill a couple of hours over a beer and some food in the restaurant...
An excellent sausage soup, a main course of schnitzel, potato and salad, all served on proper china, a beer and coffee all come to only around 10.