How bad/deep is the pitting? Microns or millimetres? If it's too deep to sand and polish out, forget it. Oil it up and go hunting.
If it'll clean up alright, follow directions on cold bluing bottle meticulously and it'll be fine.
I did an old embattled PH Safari Deluxe .30-06 a few years back, without any fancy tools. Remove stock, but leave action assembled with barrel. Used solvent and wet&dry sand paper (with water) back to appropriately clean and uniform surfaces. I finished polishing with steel wool from memory. I applied the blue with cotton swabs- about six -8 coats I think, polishing in between the first few coats. I'm sure results and expectations vary, but any Parker Hale is an oldish rifle, so when I say it should come up mint, I mean bloody nice!
Good luck mate
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