Edit 4 February 2020
Please note that this answer is now of historical interest only. For the full picture see the answer by @jcaron When are the direct Eurostar trains from Amsterdam to London planned to start?
In brief they start from 30 April 2020 from Amsterdam Centraal but only on 18 May 2020 from Rotterdam Centraal as more work on the terminal is needed there.
Further edit 26 October 2020
Note that the first service ran today from Amsterdam and Rotterdam to London.
================ historical bit starts here ==================
The situation has moved on now. The man in seat 61 has even stated a page about progress.
Basically the hope is to start trains in spring 2018 and test trains have already been running over the route. Work has stated on facilities both at Rotterdam Centraal and Amsterdam Centraal to security check passengers going to London. However exact arrangements will be subject to government approval so it may still be the case when the service starts that passengers for London will have to detrain in Brussel/Bruxelles for checks.
The article has more details albeit tentative at this stage (February 2018).
========== edit 9 February ==============
As luck would have it the day after I posted that the CEO of Eurostar rang Mark Smith (aka the Man in Seat 61) to tell him that services will start from 4 April and booking will open from 20 Feb. See his tweet here and various other tweets about the same time.
========== further edit 7 March ===========
It is now clear that although direct London Amsterdam trains will start there will be no direct Amsterdam service until passport checks can be implemented at the Dutch end. So although the trains will return they will only carry Amsterdam Brussels passengers and Brussels London. The stop at Brussels is not long enough to disembark and re-check in. More details on the Seat 61 page linked to above.