I visited there a few times, the track was literally in short sections, there was bolted fishplate joint about every 2m so could be quickly removed each weekend to dig out and build new trackbed. There was lots of temporary timber work under the sleepers for a while.
I believe the track lowering was so the ticket hall could be built above the tracks with a flat floor (and still have headroom under the new Portcullis building.
The old Westminster station had footbridges over the tracks, and the far one (Embankment end) was served by a small station entrance in Portland Stone that was built as a trial (along with back entrance to Bond Street) ahead of building the Northern lines southern extension to Morden.