Very wise of you to check availability first. I even recommended you to purchase the seat reservation before you buy the pass as even if you see available seats right now the can be gone the next minute.

Here is a good place to check the availability of pass holder seats on the Eurostar.

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

When do you plan to travel?

Thanks for getting back to me swiftly!

I plan to travel to Brussels tomorrow (2 July), and will come back to London on 3 Sun evening. 

Unfortunately it seems there is no available seat, from the b-europe.com website. :’)

The pass holder seats on the Eurostar on many departure during high season are sold out weeks, and sometimes months, in advance. 

And even the normal seats-at high inflated prices-are also sold out on many trains the coming weeks-sometimes even in 1st. Travel is booming now that people can go again after 2 yrs of being unable to