I also hired a van in Cambridge to move over to Geneva this summer. These guys were fantastic:
http://eastangliarental.com/
Cheapest place I could find, no problems with driving to Switzerland, no problems at all with the usual damage checks (the van was very new, but he wrote down at the start that it was basically scratched all over so that we know unless we totalled it that it wasn't going to be a problem!!).
We got a Luton van with a tail lift, which made loading and unloading sofas etc a lot easier.