A pair of bright chrome plated, ivory-gripped Single Action Army "Artillery" revolvers is seen in the office of the gun trading company in "Picking It Up" (S01E01). The top manager claims that these revolvers belonged to William "Buffalo Bill" Cody, whose ancestors allegedly came from the island of Jersey.
Smith & Wesson Victory
Laurence Mitchell (Derek Farr) holds a Smith & Wesson Victory Model revolver in "Portrait of Yesterday" (S01E06) when he surprises Peter Westgate (Charles Kay). Later DS Jim Bergerac (John Nettles) finds this revolver in Westgate's suitcase. Charlie Hungerford (Terence Alexander) takes a S&W Victory in "Last Chance for a Loser" (S01E07) when he hears a suspicious noise in his house at night.
Smith & Wesson Model 36
Eddie St. Pierre (Patrick Mower) holds a snub nose revolver during a night scene in "Last Chance for a Loser" (S01E07). The gun is seen only marginally, but a Smith & Wesson Model 36 seems to be a good guess.
Pistols
Inglis Hi-Power (replica)
Peter Kinthly (John Gillett) holds an Inglis Hi-Power in the climactic scene in "Campaign for Silence" (S01E04). When he drops his pistol in the grapple with Jim Bergerac, Major Furneaux (Ian Hendry) picks up the gun. The pistol appears to be a replica, very likely a non-firing one, due to its simplified appearance.
Browning Hi-Power
When Furneaux hands the pistol to DS Jim Bergerac (John Nettles), the pistol switches from an Inglis Hi-Power to a Browning Hi-Power "Type 73". This gun also may be a replica, but it isn't seen close enough for positive identification.
Walther PPK
In "See You in Moscow" (S01E05), a Walther PPK is seen in the hands of Soviet spy Belov (Christopher Rozycki). Margaret Semple (Sara Kestelman) later takes his pistol and uses it in several scenes.
Walther P38 (sawed-off)
Beaumont (SPOILER! Highlight to see description) the alias of Jacques Tabouis (Anthony Forrest) is armed with a short-barreled Walther P38 in the climactic scene in "The Hood and the Harlequin" (S01E10). The lack of the front sight allows to identify this pistol as a sawed-off P38 rather than a factory P38K. Similar pistols are seen in several British films from around the same time period, such as Brannigan and Escape to Athena.
Shotguns
Double Barreled Shotgun
Double Barreled Shotguns are seen in the hands of Kranski (Ray Mort) in "See You in Moscow" (S01E05) and Philip Bernard (Warren Clarke) in "Relative Values" (S01E09).
Single Barreled Shotgun
Lisa Reynolds (Lynda La Plante) holds a Single Barreled Shotgun in "Relative Values" (S01E09). This is a hammerless, small-caliber folding gun, possibly a Beretta Model 412 (also known as FS-1 and Companion) that was chambered in a variety of gauges, including 28, 32, 36 and .410 bore.
Rifles
Anschütz Target Rifle
Cropley (Gil Sutherland) and an unnamed person hold small-caliber sporting rifles in a photo in "Campaign for Silence" (S01E04). These rifles are most likely Anschütz models, like Match 54 or Supermatch 1413.
Machine Guns and Autocannons
Vickers
A Vickers machine gun is seen in Mr. Tuchel's private museum in "Late for a Funeral" (S01E08). It may be a replica, due to its simplified appearance.
Hispano Mk II
A Supermarine Spitfire LF Mk.V C fighter plane, seen in Mr. Tuchel's private museum in "Late for a Funeral" (S01E08), is armed with two wing-mounted Hispano Mk II autocannons.
Trivia
Spear Gun
During the underwater brawl in "Late for a Funeral" (S01E08), two of Ronnie Bishop's henchmen - Eddie (Michael Watkins) and an unnamed one - are armed with spear guns.
Carronades
A row of late 18th - early 19th century carronades is seen in the Elizabeth Castle in "The Hood and the Harlequin" (S01E10).
Footage
Documentary footage of the Korean War is seen in "Campaign for Silence" (S01E04).