Further to this thread: http://forums.pigeonwatch.co.uk/forums/topic/332281-match-the-scope-to-the-rifle/ I duly put the Hawke 4-16x50 AO on the HMR. Knowing it would need zeroing I went out this evening and set up a 50 yard range (illuminated as it was dark!). Got the elevation adjustment OK but despite counting the clicks I couldn't get the azimuth dialled in.
Further investigation found that the erector tube wasn't moving at all in the azimuth plane. I unscrewed both turrets and with the aid of a torch and a thin screwdriver, I managed to move the erector spring round to the right place again but I'm not confident it will stay there. The scope seems to be working as it should now, but by then I was too cold to try and zero it again.
On the plus side, the new .22 Sako Finnfire wasn't too far out and after a bit of tweaking, the rifle was producing nice tight groups at 50 yards (ironically using the Hawke IR scope taken off the HMR). Trigger seems a bit heavy (HMR is too light, if anything) so I'll play with that some other time.