Bulgaria

The shortest connection I was able to find on Deutsche Bahn website is still 38 and half hours. Changing trains in Bruxelles, Koln am Rhein, Wien, Beograd. It goes to Sofia. I am not sure if transit visa is needed for Serbia and I don't think (but not sure) Eurail Pass (I suppose you have it if you want to go by train) covers Serbia and Bulgaria. Btw I was in Bulgaria twice, first Black Sea shore and then hiking in Rila and Pirin mountains. Very beautiful country but sometimes you have to rough it. For the mountains we had a mountain guide who took care of everything (accommodation, transportation, food etc.). It will certainly help if you speak Bulgarian or at least Russian. Both countries are using cyrilic alphabet and English is not widely spoken yet. Good luck and have fun.

www.seat61.com/Bulgaria.htm This website gives you everything you wanted to know, and then some, about how to travel from London to Sofia via rail.

My preference would be to use budget air from London to one of the countries adjoining Bulgaria (Zagreb or Budapest? Look for the best and cheapest flight options). That way you wouldn't be facing an extremely long rail journey (and would have more time to enjoy Bulgaria!).

And if you have to use the Serbian or Macedonian rail system... I can tell you, they are NOT up to Western European standards.