There are now direct trains Amsterdam-London calling at Rotterdam and Brussels, and one can book a ticket Amsterdam/Rotterdam -> Brussels on it.
Given Schengen, how are Brussels-bound and London-bound passengers segregated?
This used to be a major, dangerous hole in the Schengen and UK borders, with trains Brussels-London calling at Lille, but was solved by confining Lille-bound passengers to the far rear coach of the train.
So how is it handled for trains from Amsterdam? The Dutch border control didn't give me a clear answer, and Eurostar is currently taking around a month to respond to emails.