From December 20014 a new fast train service is being started by Eurostar in partnership with Swiss "TGV Lyria". Initially it will run on Mondays, Thursdays, Saturdays and Sundays.
It will run from London St Pancras to Geneva via Ebsfleet and Lille and will take just over 6 hours.
In reality this won't be much slower than flying and you can take lots of luggage without incurring extra changes.
If booking via Eurostar you can specify onward trave to Aigle which is our nearest station.