Weekends are often released much later
You can check what dates tickets are released here https://www.avantiwestcoast.co.uk/travel-information/plan-your-journey/timetables#june
As you are in UK you can also get free reservations at any ticket office, bring your pass.
If you haven’t booked Eurostar yet, then do that ASAP.
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. Looks like tickets /reservation will be available later next week.
Dont worry I booked the eurostar a couple of months back!