Prob. not a P-H. They made some, but many were also made by BSA, LSA, and probably, many of the famous custom gunmakers in the UK. The .303 wasn't as potent as the "big game" calibers or even the 8mm or .318 Westley Richards.
But it was plenty potent for most animals at average ranges in skilled hands. It was and is still popular for even moose in Canada! Most African plains game are within its capabiities. You surely know that some stretched it to kill even elephants.
The rifles are rare today, I've never seen one outside of photos. I have seen and handled the postwar P-H varieties, but they were more mass-produced wth less care, although still pretty well made.
I have no idea what a nice one would sell for. They're too seldom offered to have an average range. If I had the bucks, I'd have one made on a No. 1 MK III action and fantasize that I was hunting impala or Thomson's Gazelles on the Athi Plains in the 1920's! Seriously, it'd make a swell deer rifle. But the Mauser-derived rifles are more powerful and stronger and are preferred for custom sporters today. The .303 would be mainly a nostalgic choice, evocative of a bygone era.