This has already been done for the Netherlands a few times, and is repeated every 5 or so years. See all the data in your browser here: http://ahn2.pointclouds.nl/
I think someone made a Minecraft map out of the current data, will be interesting to see what is made from the update.
It's hard to see how OS capture height exactly, I imagine via aircraft[1]. Not sure whether they are the source of the existing data the Environment agency has; I doubt it as their data has a max resolution of 5m while the government's is 1m.
[0] https://www.ordnancesurvey.co.uk/innovate/developers/minecra...
[1] https://www.ordnancesurvey.co.uk/international/knowledge/dat...
2017 is so retro, I wonder if I will be able not to use Chrome in 2018.