What is the most cost effcient way to travel our 21/2 week April vacation starting in France (Paris and Champagne region) to Switzerland (Zurich, Interlaken) and finally to London?
It sure would be nice to know your schedule, there are huge differences depending on the cities being visited. But to give a very general answer to an even more general question - use the train.
Zürich to London is a long journey by train, and you've already visited France. So I'd say Paris to Champagne region to Interlaken (via Basel) to Zürich by train (maybe include a stop in Luzern on your way), and then fly from Zürich to London.
Fly from Zurich to London, my preference. Just FYI, It's a bit longer than San Fran to Portland, including crossing the water. Would you enjoy that long of a train/car ride or prefer to fly? Lots of Europe is out of school and work for 2 weeks due to Easter holiday, so the roads/trains will be busy.