The cheapest form of transport between the 2 cities is by bus (www.eurolines.com). It can be as cheap as 18 euros one way if you book in advance.  You may find cheap flights on Easyjet (ww.easyjet.com) but remember the cost of getting from the airports easyjet uses in London (into the city) can be around 12 pounds – around 16 or so euros alone.

Bus or plane will probably be cheapest. In addition to Nomad’s suggestion look at www.whichbudget.com to see which budget airlines fly which routes.  Look at nearby cities on both ends of the trip if you can’t find a cheap flight between Amsterdam and London.  I would also check www.eurostar.com between Brussels and London.  You might find a cheap leisure fare on the day you want to travel.

I went Paris – London on Eurolines.  I will say that we had some problems with immigration and were 4 hours late to London.  Don’t go on a tight time table, but it was super cheap.

I guess you’re flying back to the US from London Heathrow, keep in mind that the distance between Heathrow and one of the other 4 airports of London is quite big and also cost some money ofcourse. British Airways and bmi offer flight from Amsterdam to Heatrow directly. The price is about 75 euro.
A flight with Easyjet to Luton, Gatwick or Stansted will set you back around 40 euro.
The cheapest (and slowest) way though is a Eurolines bus.

Ryanair.com, it does not go int Heathrow.  Stantan I think and then the train into heathrow

cool.

I think Dismanrc meant Stansted (just don’t want you to end up at the wrong airport since there are 5 for “LON”).