Flying would be the quickest way to get from London to Amsterdam. A return trip will cost you about 60 Euro to fly..just depends on when you're going and th eflight length is just over an hour. www.skyscanner.com is a great site to use to find the cheapest flights so have a look and see. easyjet and ryanair will also have the lowest fares.
If you're planning on flying then book as early as possible as the flights will definitely get more expensive or sell out completely. about 6 years ago
Its about 4 hours via Eurostar with a change of train at Ghent and will cost just over 100 pounds depending on when you book.
www.easyjet.com have flights from London Gatwick, Stanstead or Luton to Amsterdam return for around 50 pounds if you book enough in advance.
I would love to go via train and ferry (http://www.seat61.com/Netherlands.htm#train+ferry) which seems very reasonable and you can go overnight.
Or catch a coach for around the same price as an easy jet flight but it will take 11 hours!
I guess it depends on whats more important to you - time or money. If its time, then flying is the only way to go. If its money, then I would do the train to Harwich, get the sleeper ferry over and then the train again to Amsterdam. about 6 years ago