It’s definitely possible AND pleasant to avoid the plane and still go to the alps with your bike. See issue 127 for details. https://singletrackworld.com/2019/10/singletrack-issue-127-verbier-by-train/
I enjoyed reading that, I’d LOVE to take the train to the Alps the problem whenever I’ve tried to plan a route isn’t the London to Alps bit, that seems, on paper at least seems reasonably simple with surprisingly few changes.
It’s the getting to London bit:
It costs more to take a train to London for me, then it does to fly from my Local Airport to Geneva.
It would cost about the same for 4 of use to take a train to London as it would to drive from my house to Morzine, that’s fuel, tools AND crossing.
To actually take the train, I’d have to use the tube from Paddington to St. Pancrass, dragging a bike bag and case. Which sounds like hell.
I could drive to St. Pancras and park, but that seems pretty counter intuitive and would cost £300. I think there’s a Park and Ride in Kent, it’s about £50 a week, but it’s a 400 mile round-trip for me and at what point do you wonder whether if you’re really making much of an environmental saving.
I’ve come to the conclusion that the Brit side of Eurostar was designed mostly for Travel between London and Paris.