Parker-Hale ENTIRE rifles numbered up to just over 9000.
A number of Parker-Hale barrels WITH breech plugs - IOW, proofed barrels actually proofed in Birmingham England, stamped crown over BP [Birmingham Proof] and with a cypher giving the date of proof, and a description of the charge - usually 90gr of black powder, and the bullet - usually 535gr .577calibre were also stamped ion the underneath of the barrel. The breech plug will have a different serial number, as they were batch-made separately.
All this changed at around 14000, when ALL P-H manufacture ceased, and the assets were sold off to Euroarms in Italy. Any barrels remaining were without breech plugs, and could not be proofed in Italy without one. These guns began a new serial number series, of which your gun is one, with an Italian breech plug and proofed in Gardone Val Trompia - loacation of the Italian national proof house. It will also have little shield depicting the coat of arms of the city, surmounted with the crown of the Republic of Italy, and the word 'black powder only'. The date code is a couple of letters in a small square box. I recently posted a list of all Italian date codes up to 2030.
Your barrel is a P-H barrel, but as with a few of the early Whitworth rifles sold by Pedersoli, this is all there is of Parker-Hale.