May not be worth miles gathering but finding a much cheaper flight.-in this instance. I do sympathise I'm currently trying to justify a trip to northern Ireland with an airline that gives me miles but no status miles v a lcc that gives me nothing at a cheaper fare.
Try www.skyscanner.net for carriers including LCCs
The train is a really good service and if you are staying in central London as it is city centre to city centre may work out just as time efficient as flying. Check out www.nationalrail.co.uk for times and fares. Often two advance purchase single tickets work out cheaper than a return btw. Rail is only expensive if buying on the day tickets-plan ahead and book (collect tickets at the station when you arrive in London) for much better prices.
Depends what your personal value on miles is but I doubt the Paris/Amsterdam option would be justifiable.