I'd love to know the rationale for why they geoblock the UK from watching this particular documentary.

That's very odd. Here's a mirror: https://www.dropbox.com/scl/fi/phqh8xnpb2gwk3qwhk47x/Poverty...

They probably have bits of footage from British TV companies, who are fine licencing them to be shown abroad, but have either already sold an exclusive licence for UK broadcast or want to keep that option available to them.

The programme almost certainly includes content from a UK broadcaster that was licensed on the basis that it would only be used outside the UK.

Same here. The Dropbox link in the other comment was useful.

Makes you wonder if there’s a conspiracy to stop those of us in the UK watching it even though we know how awful it is at times.