The absence of military ownership or issuance markings make it very unlikely that this pistol was in British military service. However, the proof marks and the "Not English Make" marking are very strong indicators of sale for private use - formal proofing, and marking the piece as not manufactured in Britain, were legal requirements of such commercial sale (but were not a requirement for military ownership.) Actually, target shooting and such firearm-related activities were quite common in the United Kingdom until well after WWII, and 'gun control' there has not been as strict or all encompassing as many people think.
The Gun License Act of 1870 was really just a revenue raising measure since it did not restrict purchase or ownership of firearms .... rather, it required anyone wanting to carry a firearm off their own property to purchase a license to do so ..... but anyone could obtain one simply by paying the prescribed fee at any Post Office. The first 'restrictive' firearms legislation was the Pistols Act of 1903, but it simply prohibited sale or rental of a pistol to anyone not in possession of a gun license (still available on demand and payment of the necessary fee at a Post Office) or a game license, or falling within several exemptions from the Gun License Act, or able to establish they intended to use the pistol on their own property, or about to go abroad for six months or more. This was a largely ineffective piece of legislation, as you can imagine.
The 1920 Firearms Act introduced the requirement for anyone wanting to own or purchase a firearm or ammunition to obtain a firearm certificate, renewable every three years, and actually required the applicant to provide some justification for wanting a certificate .... but, of course, participation in target shooting and the like were fully acceptable reasons for obtaining a certificate. It did not apply at all to shotguns or other smoothbore firearms.
The 1937 Firearms Act modified the existing legislation in a number of relatively minor ways - e.g. raised the minimum age for obtaining a firearm certificate from 14 to 17, extended control to shotguns and other smoothbores having a barrel length of less than 20 inches, greatly restricted ownership of fully automatic firearms (following the lead of the US National Firearms Act of 1934, by the way) and transferred issuance of certificates for fully automatic firearms to the military, and imposed more regulation on gun dealers. Separately, that same year, the Home Secretary issued a ruling that "self defence" would no longer be considered a valid reason for obtaining a firearm certificate.
Things remained largely unchanged for three decades, until the Firearms Act of 1968, which brought all of the existing measures under one piece of legislation. It finally introduced the requirement for a Shotgun Certificate to own or possess long-barreled shotguns .... although, unlike a Firearm Certiciate, there was no requirement to show justification for having such a shotgun. A further amendment in 1973 required firearms to be locked up, and ammunition to be stored in a separate locked cabinet.
The current draconian firearms prohibitions and restrictions in the United Kingdom only came about with the Firearms (Amendment) Act of 1988 (following the so-called "Hungerford Massacre" in 1987) and the Firearms (Amendment) (No. 2) Act of 1997 (following the "Dunblane Massacre" in 1996.) Restrictions are still considerably less strict in Northern Ireland.