It turns out my rifle is very much like this one found in this thread @
Another Enfield #2 MK IV Trainer ... CAI Import - AR15.Com Archive
with a sleeved Parker-Hale barrel on a 1916 BSA receiver. Mine also is marked just to the rear of the charger bridge below the CAI import mark: No 2 MK4 22 U KING. But it differs in that it has the 22No2C bolt head and an AM s/n.
https://www.milsurps.com/images/impo...2sp4ejij-1.jpg
I like MVolkJs' comments in the thread and will probably describe it (underlined) the same.
"These rifles were a batch of rifles made up for the Air Ministry (that's what AM stands for).They aren't technically No.2 rifles as the No. 2 spec indicates a solid barrel, not a tubed one. What the official designation for them was I have no idea, as these were specifically Air service rifles. It's probably safe to call them
Pattern '14 .22RF No. 2 s as that was the last accepted spec to use the Parker Rifling method of conversion to .22, though that spec no longer existed officially at the time these were converted (estimated to be around 1936)"