OK, flight mavens, I need some help. Because of a series of bizarre circumstances, I have a round trip ticket to LHR that I can use this spring. While I'm in Europe, I'd like to join a friend traveling around the world for a part of his itinerary, including Florence, Budapest, and Prague. Ideally, I'd like to fly LHR-FLR, FLR-BUD, and PRG-LHR or BUD-LHR, then hook up with my return flight and head back to SEA.

I've looked at the published fares and they are astronomical for one-way trips. My question is, what is the most cost-effective way to do this? I'd like to use Star Alliance carriers wherever possible, but not if it's going to cost five times as much!