For what it's worth, Eurostar say they will be running 2 services between Amsterdam and Brussels to supplement the Thalys services.
But they don't explain the connectional arrangements at Brussels Midi.
The seat61 item shows a 28 minute wait for the through trains at Brussels, presumably for passport/security checks.
So can you travel on the through train or not?
All very unclear.
To summarise:
Eurostar will be running from Amsterdam to Brussels, and Brussels to London, with one train.
On arrival at Brussels from Amsterdam, all passengers, and their luggage, must leave the train.
Passengers from that train intending to travel to the UK must then proceed via security and border control.
The train is at Brussels for 28minutes, whence it then departs for London.
The minimum check in time at Brussels for standard tickets, is 30 minutes (45 minutes at busy times) to allow for the security and border control checks.
Therefore if you alighted the Eurostar ex Amsterdam, you would not reach check in before it closed for the onward journey (for standard passengers)*
Eurostar will therefore not sell you a ticket that officially connects you off the Eurostar arriving from Amsterdam back on to the same Eurostar departing on to London.
Therefore your options are either 1) take the earlier Thalys train from Amsterdam, which does provide sufficient time at Brussels to clear security and catch the Eurostar (that originated at Amsterdam) and is thus an official connection, or, 2) catch the Eurostar at Amsterdam, and connect into a later Eurostar from Brussels (that has not started in Amsterdam).
Simples.
* given that the check in time for Business Premier is only 10 minutes, it would, in theory be possible to catch the Eurostar from Amsterdam, alight as required at Brussels, run round to check in, check in for the Brussels-London leg, clear security and board the same train for the trip to Blighty. Eurostar won't let you book it as one journey though, presumably as it breaks the minimum connection time, so you would need to book as separate legs, and risk the connection. (ie if the train was say 18 minutes late into Brussels, it could still leave on time, and there would not be sufficient time to to get checked in).
Nevertheless (and if it's ok with the Mods) I will stand a pint to the first forum member who publishes evidence on the Trip Planning & Reports forum of them making this unofficial (but technically official) connection, with the added spice of occupying the same business premier seat (reserved as such) on both the Amsterdam - Brussels and Brussels - London legs. Appropriate photographic evidence of timings etc. required to claim the prize.