In the bad old days (10 years ago), when we got it from a well known credit check company, it came on CDs. We then moved to "automatic" updates via their rubbish, buggy software to our on-premise install. That wasn't such a huge upgrade, because as soon as you looked away from that software it would stop working.
Now we pay a different, altogether better company to access it via a web service. I would expect that the speed of updates through to websites is now mostly as good as the frequency of PAF releases. Unless this has changed recently, the PAF isn't created by Royal Mail itself, it's outsourced to a company called AFD based on the Isle of Man.
My only complaint with the service we get now is that the value is quite poor - our total cost is somewhere around 30p per lookup on average for addresses which I suspect are rarely even used in our line of work.