It is not well known the first "military issue" repeating handgun acquired by the United Kingdom was, in fact, the Model 1851 "Navy" Colt!
With the Crimean conflict looming large, The Board of Ordnance/War Department purchased approximately 23,700 London Colt Navy revolvers, beginning in March of 1854. Almost 10,000 of them went to the Royal Navy, and approximately 5,000 went to the Crimea for Land Service, primarily for use by officers and sergeants major of infantry, but also with "emergency issue" authorised to Lancers, and to Dragoon and Hussar sergeants major and trumpeters, in lieu of the regulation single-shot percussion pistols mentioned by Gordon .....
It was not until 31 August 1855 and 3 January 1856 that contracts were placed, respectively, for British-designed revolvers - i.e. 300 "Revolvers, Dean & Adams improved on Beaumont's principle, with appurtenances" and 2,000 "Pistols, revolving, Dean & Adams' patent, with Lieutenant Beaumont's improvement, 54 gauge".
In late 1868, conversion by J. Adams of existing Dean & Adams percussion revolvers for self-contained metallic cartridges was approved (ultimately becoming known as the Mark I Adams) and in 1870, the Mark II and Mark III Adams built-as-breechloader revolvers were approved. However, as Gordon has indicated, Adams revolvers were not approved for issue to cavalry until 1878.
Interestingly, Adams revolvers were adopted in for issue to Canada's North West Mounted Police in 1874.