The BSA Century........
This rifle was something of a half way house and was a compromise between the "Sportsman" series of bolt action .22 Sporting Rifles and the Martini actioned target rifles that BSA produced.
Not certain but it may well have been a rifle which either filled as a stop gap between the older BSA Martini and the
later "International" model's. Alternatively it may have been built to be something of a challenge to the growing preference for the "bolt action" as opposed to the Martini action. The Anschutz models were eating into the BSA market with their bolt action rifles.
Basically it looks like a Sportsman Five bolt action type receiver fitted with a bull barrel.
Fitted with diopter type target sights (and the few I've seen had blocks inlet into the barrel for a scope)
Unusually for a Target rifle it was fitted with a magazine (clip to you guys

)
They are not really common, nor difficult to find a good one (with sights) would cost £ 100 -150 (about $150 - 225US)
Hope this helps.