How to get from Brussels central to Brussels Midi/Zuid

It’s only a few minutes taxi ride or by train. Type it into the Rome2rio App.
I took a cab.

Perfect. Thank you Diane!

Your second ticket of the day (sounds like ... ) INCLUDES the right to take any local train (6-8 or more per hour in daytime) from any of the three downtown Brussels train stations to Midi/Zuid. This applies to the regular long-distance trains, not to the Metro. Centraal is conveniently near Grand Place, and has an escalator in that direction. Some stairs later, AFAIR.

Do not overlook the mandatory 60-90 minute check-in (whatever they tell you) for customs and immigration at Eurostar. This is not fudgeable, and they will refuse boarding if you don't come reasonably early.

You didn't describe the character of your first ticket, but virtually all tickets to Brussels are either good to all three stations, or if the train only goes to one, you get that kind of Eurostar deal from other premium trains like Thalys. Many Belgian trains stop at all three stations.

If you are at Brussels Centraal, taking a taxi to get to Midi/Zuid is to be honest one of the worst ideas I've heard. Just take any of the frequent southbound trains. Quick and easy. And no need to buy a ticket for that trip, your Eurostar ticket will be valid on the Centraal-Midi/Zuid trip.

All great information. Thank you - love this forum already

From what direction do you arrive into Brussels Central? It makes a difference if you come from Brussels Airport or from Bruges / Ghent.

Nothing to do with brexit - there has always been a significant check in deadline at Eurostar - they have always done Belgian exit formalities and UK entry formalities (UK has never been in Schengen) after the check in formalities and the security check. Don't be late.