eurostar

There is a passport check at St Pancras station. If you're saying you have another train to catch 30 minutes after you arrive, it's not enough time, you won't make the connection.

Thanks. I can pay more and get earlier train from Brussels. I thought they might check us on the train

I've taken the Eurostar train from Paris to London many times. Passport control for England (Britain) is on the Paris end. I assume that your passport will be checked in Brussels before you board the train. In that case, 30 minutes should be enough time to catch your connecting train. The connection may involve some walking to reach your second train, so hustle along.

You are checked at the boarding end, NOT when you arrive.
Roger

My last journey on the Eurostar was in June of 08, Lille to St Pancras; the train I hopped on originated in Brussels. My passport was stamped three times: French Immigration in Lille, UK Immigration in Lille, and UK Immigration at St Pancras. Granted it doesn't make any sense for the UK Border folks to check/stamp it twice, but it did happen during my journey....YMMV.

There are no passport checks at St Pancras. There was for a short time a couple of years ago, when as a cost-cutting measure UK border guards were removed from Lille station and they checked all passengers off trains stopping at Lille when they arrived at St Pancras. But that caused so many complaints about immigration delays at St Pancras that they were forced to reinstate the UK passport control at Lille.

My experience of arriving at St Pancras from Paris is that you get off the train, walk to a down escalator, walk some more thru a gauntlet of security people (they just look at everybody passing by), then exit to the main corridor of the train station. No delay, no passport control. I've traveled Paris-London about 9 times in the last 9 or 10 years. Of course, it was Waterloo Station previously on the London end. In every case, I went thru British passport control in Gare du Nord in Paris. To connect to another train, there would be more walking.