Begin with Alps first and then to Paris and London or Vice Versa?

Fly into London and out of Zurich or vice versa, for one thing. Don’t backtrack. Also, unless you have specific sites to see in Zurich, skip it. Luzern and the Lauterbrunnen Valley are far better places to spend time.

How many nights do you have for the trip?

I have run into this kind of dilemma before. I've solved it based on such factors how much the flight costs for example is it cheaper to fly into London roundtrip or open jaw into London out of Zurich for example. Also I look at what happens to be going on culturally i.e. festivals, exhibitions, and night life concert stuff to do besides sight seeing.

My last trip I flew into Amsterdam and back from Milan via Dublin after spending time in the Berner Oberland

When are you traveling?

If you are going in a shoulder season, Paris and London will be fine any time but with Switzerland you might juggle things so it's at the end if you are going in Spring or on the front end if you are going in Fall.

Definitely not backtracking... my reward tickets allow me to fly into London and out of Zurich and vice versa

4 nights in alps (not Zurich.. just day and move on to Luzern / Lauterbrunnen area
3 nights in Paris
3 nights in London

Thank you everyone... End of July

Given your 4 nights/3 nights/3 nights plan, I would drop any idea of Luzern and go to the Lauterbrunnen Valley immediately. I would also drop London and add time to Paris. It’s just so too much to do both cities so fast and a lot of train time for 10 nights on-the-ground.

Check the price for taxes on your reward ticket. If I recall correctly, there is a pretty high departure tax flying out of London, but much lower taxes for arrival to London.

If price is not an issue, I’d put the place you are most enthusiastic about at the end.