Which train pass is best for London, Belgium, Amsterdam?

"Anthem" or Antwerp?

Antwerp

Thank you for correction.

It sounds like you have the important dates (the days of the cross-border trains) fixed. In that case, you don't need to buy a rail pass; it will make sense to buy some of the longer-distance tickets ahead of time, which will mean buying tickets for a specific time and train, but since you have a good idea of your itinerary this shouldn't be a problem.

Long-distance trains you should buy as soon as you have finalized your dates (these trains have dynamic pricing):
- London to Brussels on Eurostar
- Brussels to Amsterdam on Thalys -- if you don't want to commit to this date, you can also take the cheaper (though longer) Intercity trains, which don't vary in price
- Amsterdam to London on Eurostar

Domestic train travel within Belgium does not vary in price, so you can just buy these tickets on the spot when you need to.

There isn't a train pass to cover that area. And most train passes these days provide convenience and not saving. For your limited travel a train pass would not be economical.

Thank you Andrew. This information is very helpful.

Thank you Frank. Appreciate your input.

Our dates are confirmed.

Since you are doing a day trip to Antwerp, you might consider doing it as a stopover on the way to Amsterdam. It is about 1 hour from Brussels to Antwerp on an IC train, then a little less than 2 hours for an IC train on to Amsterdam. You can store luggage in lockers at Antwerp Centraal.

The Eurail Global pass "covers" all those routes but, since the Eurostar and Thalys trains require rather expensive seat reservation fees (around $35 each) in addition to the pass, I'm not recommending it to you.