Because every house has a single, unchangeable IP...?

You clearly never worked in an ISP.

I definitely did not work at an ISP. But what I said doesn't require a static IP per house. Just GeoIP so non-UK residents are treated differently (unless they VPN).

The target is not to determine whether the client is in the UK, but whether the client is a specific license-payer or at a specific address. GeoIP doesn't help to get either of those datapoints.

How does that get them subscription estimates?

Then they can make sure people in the UK have a subscription account.

Enforced by a proprietary app?

Yes, called iPlayer[0].

[0] https://en.wikipedia.org/wiki/BBC_iPlayer

Or Sounds which is basically the audio version of iplayer