Given that OSM has a lot of building addresses and locations (at least it has building names and numbers and the streets they are on, plus their outlines) I wonder how much of the PAF could be recreated from the data in CodePoint Open combined with OSM. If adding more house numbers etc to OSM would help improve that then it could be crowdsourced quite quickly via Street-Complete or similar.

For the purposes of the quick address lookup it doesn't even need to be 100% accurate. If a property is incorrectly listed against two postcodes it won't really cause problems, so the lookup could err on the generous side