It's easy to do it, the Production Designer did a great job. The room was a set, there was head room beneath the suspended floor for the task design team to feed the masks through.

Hello David Icke, welcome to DS

Ha ha ! Hiya.

This was my first thought from the moment they stepped in the room.

It's also possible every podium had both masks inside and the production gallery just controlled electronically which mask each celebrity received. In fact, probably this.

Borehamwood studios have the height to do this, look at the dimensions on their website might explain why the ceiling and walls looked to be "curtained"...Not the most expensive Art Departent job to fly a false floor, just a bit a scaffold and board.