"experts" have been saying that East Anglia has less rain than the Sahara for many years
I don't know this particular claim, but East Anglia is definitely the part of the UK that gets least rainfall. In 2022 it has been particularly dry, with February being the only month that was wetter than average, and with virtually no rain at all in July and August.
East Anglia is expected to house many more people in the next few years
That's already happening. Comparing the 2021 and 2011 censuses, three of the top six local authority areas for population growth were Bedford, Peterborough and Cambridge.
In my view availability of water is the most significant constraint on future economic development.
I wonder what they will do with the earth removed?
The middle of the Fens is a strange place to build a reservoir from an engineering perspective. I suspect that earth dug out of the hole in the middle will be used to create banks round the outside to keep the water in.