Really? Via what route? I spent all last night looking and could not find a decent option. (Though keep in mind I'd only want to do 2 days).
We've booked this for £240 ish. Cheapest I could find direct from UK was £420.
Tues: Stansted to Hamburg to Istanbul, 3hr connection - Ryanair and Pegasus
Thurs: Istanbul to Bucharest to Gatwick, 3 hr connection again - Pegasus and wizz.
Routes via Berlin were available but it was getting into Istanbul dead late.
Fly to Sofia and there's a sleeper train