Combine it with a cycle tour. I did this last summer. 10 days to Geneva, and then another 2 to Chamonix. Spent 10 euros a day for food between 3 of us. Wild camped the entire way for free. So I make that 40 euros for food over the trip. You'll have to pay a tenner or something for the ferry, think DFDS were the cheapest.
In reply to Boulderdash86: Best = fly. You can fly from Exeter to Geneva. Book well in advance and it's quite cheap. Including luggage it cost me ~£80 return last year. You then have to pay for a transfer so about £120 overall.
It costs about the same as the coach but doesn't take 20 hours. Definitely worth it in my opinion.
National Express do an open return coach journey for £100. You can take as much luggage as you can carry, and it takes you London-Cham in about 18 hours. The key point is that it's an open return. If the conditions crap out and you want to come back home, give them a call and they'll schedule a pick-up a few days later. I've done it three times now (take an full iPod/book and some friends - it can be deathly boring) but I'd keep doing it.