Is 2 weeks long enough to go to London, Amsterdam AND Paris?
London is quite big place so your looking at 2 to 3 days there if you try and get quite a lot put into them days you can do already 2 to 3 days per trip. You be able to so quite a lot have fun!
If you plan it out right I can be, but you will be on the move 24/7. It's exhausting, and you can't really fully enjoy anything. Most of your trip will probably be on trains. So I suggest to give yourself more time, or eliminate Amsterdam because its out of the way of London and Paris. But it can be done.