In "The Sign of the Broken Sword" (S03E04) Webley .38 Mk IV revolver is carried by Lt. Anthony Graham (Steven Miller). In the flashback scene in the same episode David Rawlings (Jamie Ballard), at that date a captain, holds a Webley. Two Webley revolvers are seen in "The Lair of the Libertines" (S03E08).
Webley .455 Mk VI
A revolver that appears to be a Webley .455 Mk VI is used by a bank robber (uncredited) in the opening scene in "The Paradise of Thieves" (S03E13).
Enfield No.2 Mk.1*
An Enfield No.2 Mk.1* revolver is the murder weapon in "The Truth in the Wine" (S03E09). The revolver is correctly identified in the movie, and Colonel Anthony Forbes-Leith (Daniel Ryan) says that he preferred a Webley during his war service as Enfield has an insecure hammer.
A starter revolver that appears to be a Bruni Olympic 6 is seen in hands of Arnold Francis (Mark Lewis Jones) in "The Time Machine" (S03E11).
Pistols
Walther P38
A Walther P38 is the murder weapon in "The Last Man" (S03E05). A P38 is seen in hands of Dr. Barashi (Michael Culkin) in "The Lair of the Libertines" (S03E08).
Browning Hi-Power
Two Browning Hi-Power pistols are seen in "The Lair of the Libertines" (S03E08). Count Fiskon (Nicholas Le Prevost) and Dr. Barashi (Michael Culkin) fire one of these pistols in turn. A Hi-Power is also seen in hands of Syrus (Ace Bhatti). These pistols have "Type 73"-style hammer spur that doesn't match 1950s when the story takes place. A close view of a pistol also reveals a different shape of slide serration. Maybe these Hi-Powers are some modern blank firing replica (not airsoft as one of them is seen firing and cycling). Same prop is seen in Seasons 4 and 7.
Luger P08
A Gestapo agent holds a Luger P08 in a flashback scene in "The Judgement of Man" (S03E10).
Makarov PM
A Makarov PM is carried by Harriet Greensleeves (Natasha Little) in "The Owl of Minerva" (S03E15) (a really strange choice for 1950s rural England). In one scene she gives it to Jock Hamilton (Ron Donachie). Inspector Sullivan (Tom Chambers) disarms Harriet in the climactic scene.
Submachine Guns
MP40
MP40s are seen in hands of German soldiers in the flashback scene in "The Judgement of Man" (S03E10).
In "The Sign of the Broken Sword" (S03E04) Lee-Enfield No.4 Mk.I rifles are seen during the ceremony in local barracks in hands of Lt. Anthony Graham (Steven Miller), Col. Laurence St Clare (Angus Wright), Sid Carter (Alex Price), and soldiers.
Lee-Enfield No.1 Mk.III*
Lee-Enfield No.1 Mk.III* rifles are seen in hands of British soldiers in the flashback scene of Dunkirk evacuation in "The Sign of the Broken Sword" (S03E04).
Small Caliber Bolt Action Rifle
Alfons (Philip McGinley) is seen with a single shot bolt action hunting rifle (probably of .22 caliber) in "The Kembleford Boggart" (S03E07). Something like Remington Model 33 seems to be a good guess.
Winchester Model 70
Winchester Model 70 with sniper scope is used by Anna Damiache (Rae Baker) in "The Lair of the Libertines" (S03E08).
Other Weapons
Barnett Wildcat Crossbow
Barnett Wildcat with a sniper scope is used by Anna Damiache (Rae Baker) in "The Lair of the Libertines" (S03E08).