Once you've removed the worst of the pitting, you can save a lot of time an elbow grease by using a simple polishing kit which attaches to a regular electric drill.
Caswell's have a handy downloadable polishing guide on their website. I fixed the drill to a workbench and then move the piece over the appropriate wheel. After all the hard work with papers this is the fun bit!
I bought one of these when doing the FWB 150, £10 well spent, especially if you intend doing other rifles. It was in a similar condition to your Falcon, and needed the 80 grit treatment to start with then through the grades and finished with the polishing kit.
End result.