What I'm noticing, as the body of data grows, is that each day will probably see at least 10 noticeable layers of 'lava' before the incremental increases become insignificant.
For example, if you look at April 1st, you can see 8 shades of blue, 8 noticeable layers of 'lava', each representing one of the last eight days of NHS timestamped data getting properly backfilled retrospectively into the date they occurred, April 1st. And there will probably be another two noticeable layers laid before it's done.
This 'ten layers till done' gives a rough idea of where the true trajectory will end up.
Everything to the left of the blue marker on the graph is complete-ish.
What you see there, to the left, is the true trajectory of England's deaths, timestamped into the days they occurred.
Everything to the right of the marker is not yet complete, and will continue to grow until you can see 10 layers or so at which point it will be the final picture.