That's why it is interesting that there is a precedent set by the Disneyland trains for having immigration and customs on the UK side for incoming trains.
If the only thing happening at Marne-la-Vallée is a security check, this is governed by the Intergovermental Commission that sets the rules for the tunnel - and as DB showed, they can be challenged and did respond to logic.
No, there is an exit immigration control by the French
Police aux Frontières at Marne-la-Vallée.
Customs checks by HMRC have always been performed in London, irrespective of the origin of trains - this is not something special to Disney runs.
More information:
https://publications.parliament.uk/pa/cm201213/cmselect/cmhaff/71/71we05.htm
Once again, the rules for the immigration and border controls are governed by
treaties or agreements between nations.
DB challenged rules related to fire safety and train characteristics, but not immigration or border control provisions.
In these matters, the inflexible party is - and has always been - HMG. I daresay that in the current atmosphere of total chaos regarding Brexit, amending these protocols will be the last thing on the minds of the Home Office.
Now to help answer that, a quick question from me: Is there such a thing as a Brussels-Lille or Brussels-Calais Eurostar ticket?
Brussels-Lille yes,
Brussels-Calais no.
But these "Schengen" passengers travel under very specific arrangements.
In the past, Eurostar sold Paris-Calais tickets - and after 2002, passengers on these services had to comply with all requirements for entry into the UK. Kafkaesque don't you think?