Manny, get yourself one of the BSA 12/15 martini single shots. Especially if they have the parker rifles lined barrels. You will not be disappointed. Mine has a trigger that breaks like the proverbial glass rod. Frank
The BSA's unless someone has neglected the barrel shoot superbly in their original BSA form without the need to "Parker Rifling" the 12/15 Centurion had to shoot several five shot groups of 1" on the BSA 100 yard test range before being marked Centurion and that was with the ammunition of the time.
This my own BSA 12/15 which has the Bull barrel profile:-



original Bore no liner required.


On Bisley's Short Siberia 100 yard point. Short Siberia is a 200 yard range.
Of course the British firm of BSA also made magazine repeater rifles in .22 L/R like these two:-

Top is the Super Sport Five which is fitted with a Weaver K3W in the photo. This is the later version with dovetail grooved receiver the earlier ones were plain round topped (I have one of those as well) they use a 5 Rnd detachable magazine which are difficult to find and expensive when found now as it seems some people adapted them to use in another rifle

. The Super Sport Five has an adjustable trigger which cane be adjusted to be two stage or single stage. Stock is walnut:-


The barrel is of medium weight:-

Magazine:-

Reciever

Parker-Hale made a couple of receiver sights to fit these and BSA D&T's the action at the factory for them. BSA also made a single shot target version called The Century.
The lower rifle is the Sportsman Five which used a different 5 Rnd magazine to the Super Sport. The Sportsman range included the Sportsman a single shot rifle, the Five with detachable 5 Rnf mag, the ten with a ten shot under barrel tube and the Fifteen with a 15 Rnd under barrel tube mag. These are cock on closing the action is based upon the old BSA Military training rifle of the early 1900's. The Super Sport being later is cock on opening. The Sportsman has the twist and turn bolt tail safety.
The barrels on these BSA's are very good being cut rifled and lapped as standard at the factory. Hammer forging did not come along until later on.
If you come across one of these even though it's not American they are very well made as were most rifles from reputable manufacturers of the day. The Sportsman series dates from the 1950's and the Super Sport from the 60's