TL;DR - These appear to only be bookable on the website, and must be booked more than 1.5 days before departure, but are a fixed amount as shown in the screenshot
These tickets are a little bit special, in many ways, and seem to be rather difficult to actually book. The prices are given on the Eurostar Belgian website (but not most of the other Eurostar sites!), and are €25 / £24 for a non-flexible ticket.
If you look on the Eurostar website before mid afternoon two days before travel (exact time TBC), you will be able to see and book these tickets. For travel on a Thursday, that would mean booking no later than mid afternoon Tuesday. After that, including during the evening 2 days before, they all vanish from the Eurostar website, and only the Thalys tickets remain. (The website will also only offer non-flexible tickets, despite the ticket options website stating that semi-flexible tickets should exist too)
You might think you could book these by phone, but I would advise against even trying... I rang the Eurostar UK booking line, who initially denied they even had trains running between Brussels and Lille, instead attempting to convince me that I was confused! They then changed their mind and said the trains ran, but you couldn't buy a ticket. When I pointed out their website sold them, they said that was a mistake, and it shouldn't. They point blank refused to believe they sold tickets for their own trains on this route, and told me to try ringing SNCF to buy them (seriously!)
SNCF unsurprisingly said to ask Eurostar, and offered my tickets instead on the TGV 30 minutes before I wanted to travel. Next up was Eurostar Belgium, who suggested I tried their website, or tried ringing the UK. They said tickets did exist, but that the Belgian call centre wasn't allowed to sell them.
Finally, I headed to the Railteam booking office in Brussels, just by the Eurostar checkin. They said that they are not allowed to sell Brussels to Lille Eurostar tickets, only Brussels to the UK ones. They said that the tickets can only be booked online, only on the Eurostar website, and only until "some point" two days before travel. (They happily sold me a TGV ticket to get to Lille)
So, verdict seems to be:
- In person - no
- On the phone - no
- Online - yes, but only until late afternoon 2 days before travel
Quite why Eurostar are so strange about these tickets I don't know, and quite why the Eurostar booking teams are so useless about them I don't know either, but if you really want to book these tickets despite Eurostar's best efforts to persuade you otherwise then online is your only option