There were two kinds of Mannlicher – Schoenauer takedowns once available in the UK. First, the detachable stock type as offered as a factory option by the Steyr factory and described by Rothhammer and others.
On the other hand several British gunmakers converted M-Sch actions to a detachable barrel mode. Here is mine (again), a 1903 in .256 Gibbs aka 6.5x54. Built by George Gibbs, Bristol, on a 1905 dated military production action. Gibbs screwed the barrel hand tight into the receiver and locked it in place with an elongated front guard screw. For detaching the barrel you need a turnscrew (= a British screwdriver). Loosen the front guard screw several turns. Now barrel and foreend may be screwed off the action.

Other gunmakers like Fraser used an additional thumb screw in in the left side of the receiver ring to lock the barrel in place.
Westley – Richards advertised another, more elaborate design of a barrel take down M-Sch in their 1912 catalog. W-R altered the receiver ring extensively and brazed on a reinforced extension. Their barrel had two locking lugs just like the bolt, locking it into the receiver. After opening a latch on the foreend, the barrel could be pulled out of the action after giving it a quarter turn. Btw, this W-R patent takedown system is a twin, if not a plain copy, of the 1880 German patent held by Schmidt & Habermann, Suhl.