Rifles
Enfield Pattern 14 (P14) - Used as a marksman weapon until the No.IV Mk.I(T) was introduced, also issued in large number to the LDV.
M1917 Enfield - Issued to LDV.
Martini-Enfield - Used as a reserve arm by Commonwealth troops from India, New Zealand, etc.
Lee Enfield

Submachine Guns
Thompson - US Submachine Gun in use until creation of Sten gun in 1941

Machine Guns
Bren light machine gun - Light machine gun for infantry use introduced in 1930s and used throughout the whole of the war.
Browning Automatic Rifle (BAR) - Issued to Home Guard
Lewis Gun - In service with some infantry at outbreak of war in small numbers, issued to British Home Guard for the rest of the war.
Vickers "K" machine gun also known as VGO - Fast firing aircraft machine gun, used in specialist roles on Long Range Desert Group and Special Air Service vehicles in North Africa, as well as a short-lived infantry machine gun with the Commandos.
Vickers machine gun - Standard medium machine gun of the British Army since 1912.
Browning M1919 - Mounted on many lend-lease vehicles.
Browning M2 - heavy machine gun, mounted on many lend-lease vehicles.
Besa machine gun - in 7.92 mm BESA and 15 mm BESA forms used as armament on British-built tanks and armoured cars only.
Vickers-Berthier - Light machine gun adopted by Indian Army pre-war and used by Indian Commonwealth troops.

Handguns
Enfield No.2 Mk.1 Revolver
Webley Revolver - many marks in .38 and .455 calibres
Browning FN-Inglis "Pistol No.II Mk.I*"
Colt M1911A1
Webley No.I Mk.I - Automatic pistol in .455 inch. Issued to the Royal Navy
Smith & Wesson Model 10
Colt New Service
Colt Official Police.

Grenades
Grenade, Hand or Rifle, No.36M Mk.I "Mills Bomb"

Infantry Anti-Tank Weapons
Boys Anti-Tank Rifle

Other
Smatchet
Kukri

Anti-Tank Gun
Ordnance QF 2-pounder

Guns and Howitzers
BL 4.5-inch Medium Field Gun Mk. I
BL 7.2-inch Howitzer Mk.I (Introduced 1940)
BL 8-inch Howitzer Mk VIII (Replaced by above in 1943)
BL 60-Pounder Gun
M116 Howitzer (US Supplied Mountain Howitzers)
QF 3.7-inch Mountain Howitzer (British made)

Anti-Aircraft Artillery
40 mm Bofors
QF 3 inch 20 cwt
QF 3.7 inch AA gun
QF 4.5-inch Mark 1 to Mark V

Mortars
2-Inch Mortar
3-Inch Mortar

Light Tanks
Light Tank Mk VI
Light Tank Mk VII Tetrarch

Medium tanks
Vickers Medium Mark II - Small Scale use in Africa

Cruiser tanks
Tank, Cruiser, Mk.I
Cruiser Mk III

Infantry Tanks
Tank, Infantry, Mk.I, Matilda I (Phased out in 1940 for Mk III Valentine)
Tank, Infantry, Mk.II, Matilda II
Tank, Infantry, Mk.III Valentine

Self-Propelled Guns Unsure on timeframe for these two, placing them here as they are the only one that don't have defined dates for their Lend-Lease starts.
T48 57 mm Gun Motor Carriage - 680 provided by Lend-Lease from America. Many had gun removed to convert them back to Armoured Personnel Carriers.
Multiple Gun Motor Carriage M14 - Provided by Lend-Lease from America. Many had guns removed to convert them back to armoured personnel carriers.

Other Armoured Fighting Vehicles
Loyd Carrier
Half-track Car M2

Utility Vehicles
Willys Jeep
"Tilly" - utility versions of civilian cars.