Whithout any specifications of time and date/preferred travel moment, nobody can properly answer your question. 

OK! Looking to travel London to Amsterdam 28 May, return 29 May.

There is a limited number of pass holder seats on the Eurostar between London and mainland Europe. On popular departures and during high season those sell out weeks, and sometimes months in advance.

The best place to see the availability of passholder seats and make reservations on the Eurostar is 

https://www.b-europe.com/EN/Booking/Pass#TravelWish

If you don't get any result, press "later trains" and eventually you will find the next available connection. 

If you have a mobile pass you need to generate a Pass Cover Number in order to make the reservation at b-europe. You do that here in the PCN generator:

https://community.eurail.com/news-and-announcements-39/pass-cover-number-generator-is-live-5653

Thanks @AnnaB, that’s a great tip. There are no results for my dates, which is consistent with what Eurostar says. I just wish they could tell me if tickets will be available later or not. I guess I’ll assume not and make other plans.

The information on the Eurostar website says that there are no trains available on the 28th of May so either all trains are full or there is some error in the system. There should be pass holder seats available on the 26th and on the 29th. There are pass holder seats from London to Brussels on the 28th and from Brussels there are hourly IC trains to Amsterdam.

The cost for a normal Eurostar ticket frpm London to Brussels is only 57 EUR on the 28th so it will be more expensive use an Interrail pass if you consider the seat reservation cost of 30 EUR and the cost for a travel day.

@papanoob No trains to Amsterdam found indeed, but there is normal service and plenty of availability from and to Brussels on those dates.

There is an hourly intercity service, without seat reservations between Brussels and Amsterdam. I advise you to book Eurostar until Brussels and continue your journey there with the hourly direct IC to Amsterdam.

I think there are some engineering works in the pipeline on those dates, so timetables of the Eurostar are to be confirmed. Or these Eurostars are already fully booked. Which would be weird, so far in advance. But you never know

But the IC Brussels-Amsterdam and the other way around seem to have normal service on your desired travel dates, so a very good alternative for you.

Thank you!

Eurostar releases pass seats 180 days ahead and I have never seen reports that extra seats have been released, but since Eurostar occasionally increase capacity that may happen.

There are very few services that progress from Brussels and, although I don’t know whether Eurostar take fixed numbers for Amsterdam, Brussels and Lille, or whether it is first come first served for the three stations it means there are only a small number of seats through to Amsterdam from UK.

The weekend of 26 - 29 May is a national holiday so demand will be high from Friday.

Note: to Brendan: NS is so short on staff-also for IT, that IF there are works, the revised timings will only be shown 10 days ahead-if they even manage that.  So I just add; IF €* states it cannot reach AMS due to works, there is a big chance that these hourly iC trains also do not run-or via other routing (more likely). But AMS is now, since the UK-EUrocrats are no more, way more populair for €* as BRU is/was and it has just 3 trains/day and BRU ev 1 or 2 hrs. Has also to do with the needed border check staff due to all this isolationism the UK has chosen itself to be in.

Engineering works seem to be announced until the end of April as of today, on the Thalys and B-Europe website. So I guess that in a month or so, there will be more clarity. Thalys is also not open for booking too on aforementioned dates between Bxl and Ams. 

But there are a lot of engineering works planned in February, March and April. So it's likely to these continue. Almost every other weekend there are works, with detours or trains limited to Rotterdam.

So if you just want to spend a quick outie to Amsterdam, from London, best choose another date (during weekdays, usually no works) or just try to have a bit more time in Amsterdam, compensating for the (very likely) longer travel time. 

Can you please please stop suggesting the whole of the UK chose to leave the EU. Almost half of us voted to stay in the EU and it is getting towards 60% now accept it was a less than great idea. Unfortunately we all have to work within the situation and pass on how to do that in a constructive way.

Remember Eurostar is a business and it adjusts capacity in line with demand and ability to process passengers in good time, not to mention finding slots through the tunnel.

So yes one factor at all E* stations is border control capacity, which was there before Brexit as the UK was not part of Schengen, but now requires passports to be stamped rather than looked at to manage the EU Schengen 90 days in 180 rule. Amsterdam is slowly increasing capacity but for the moment a change at Brussels is still a real option once the trains to and from AMS are full.

Until things change we all have to accept the way Eurostar (and many other operators) manage their Interrail business and keep our advice balanced and temperate and not frightening off people with extreme statements.

You obviously manage to travel well across the whole network within those operator driven practices, so please pass it on in a way that allows grown adults to enjoy the planning and travel of a rail based holiday.