I am not sure whether you want to do all in one go, Amsterdam to London within 24 hours or so, or step by step, stopping for a couple of days in each location mentioned.
If traveling Amsterdam to London in a short period of time, look into the 'Each Dutch station to London' option on the Eurostar site.
I think you get 24 hours before the Eurostar train to make use of the first leg of the ticket.
If you have a stop of several days in Belgium, you might consider the 'Each station in Belgium to London'.
Tickets bought within the Netherlands costs the same whenever you buy, except Thalys trains, and for the Dutch leg, I would not bother with looking for cheaper options. You might see if you (by then) can buy online, otherwise, if you have the time to collect coins, you can still pay for the tickets by coins in many of the machines. Or pay the €0.50 extra and buy from a ticket window.
For Amsterdam or Rotterdam to Antwerp or Brussels, I would try to buy online from the Dutch site, or the Belgian site. Ticket prices might be cheaper online but a recent check did not proof that. You need to print the ticket, as far as I know, but new technology is introduced.
If buying online is difficult, the company is not known for being tourist friendly, you might want to wait till you are in the Netherlands. As said in the comments, you do not pay less when you book early. And while in the Netherlands you might find they updated the system or you might find a Dutch person willing to help you with the payments.
I am not as familiar with the Belgium system, but as far as I know you still get service, without extra costs, at the ticket windows in Belgium. And there as well, buying early will not be cheaper. But they do have several tickets that work for repeat or group travels, worth asking at the station if no answer here shows up. And they do have a good website as well. Keep in mind that buying your ticket in the train will cost you 7€ extra. If you forget to tell the train conductor, a minimal fine of 75€ is added.
And one last site that is always more helpful than Rail Europe, the Man in Seat Sixty-One, in this case the link to the Netherlands page. You can use the instructions 'the other way around' and there will help for buying tickets in the country. (In this case they send you to the same Belgian site I mentioned above.)
You might see that I did ignore the 'buy railpass' option. I did not mention it as you found already that it is more expensive for this kind of travel. The same goes for the 'discounted one day' passes for the Netherlands, for sale in some shops, they are not cheaper compared to the Amsterdam to Antwerp (Dutch part thereof) tickets. And the 'discount prices' you find on the website of the Dutch railways, they are only available if you buy a year pass, no use for you. And they do not give discount on the international tickets.
For the Amsterdam to Rotterdam leg, also see this question.
The new hall of Rotterdam centraal station, the location of a tourist information office as well as of shops, but the main activity is still travel related.