Best way to get from England to the Netherlands

If it were me, I'd fly from a London airport to Rotterdam and then drive or take the train up to Wassenaar. You can take buses but it takes a very long time - I've done this from London to Amsterdam and won't do it again. I believe British Airways and KLM both fly between Rotterdam and London. It shouldn't be more than $150 - $200, maybe cheaper. Sometimes I wait until I'm in Europe to buy my within-Europe tickets from a travel agency as they often can get you cheaper fares. Depends on how flexible you can be with your dates.

You might consider train. Taking the Eurostar to Brussels, then numerous options from there. Overall it would likely be quicker, for low cost tickets you would want to book the Eurostar tickets as soon as possible, the tickets from Brussels to your destination less important.

One very interesting way to get from London to Amsterdam is to take the train from London Liverpool station to Harwich International Terminal (It's a ferry terminal). Trip takes about 1hr40min. Take the Stena ferry from Harwich to Hoek van Holland (Hook of Holland). Ferry departs at 23:15 and arrives at 7:45. The following link shows a snapshot of your transportation options from Hoek van Holland to Wassenaar. http://gyazo.com/4ae4664d0b0d4f13c5b2ed1fb8a8ae07

All of these options are fine. I think the flight will probably be less in travel time.

Ashford - London = train to airport (about 40-60min)
London - Amsterdam = Direct flight to Schipol airport (1 hour)
Amsterdam - Wassenaar = train to Leiden and bus to Wassenaar (about 30-45 min total)
The Eurostar train will take roughly 4 hours to Amsterdam plus another 30 minutes to Wassenaar. There isn't really a wrong way to go. The Eurostar tickets can be expensive unless you get advanced purchase discounts. Otherwise, consider the flight as you can get cheap tickets on www.skyscanner.com and the local trains will be pretty inexpensive.