British Forces:

Force B
BB Renown
  Vice-Admiral Sir James Sommerville
CV  Ark Royal
      800 Sqn. – 12 Skuas
      803 Sqn. – 12 Fulmars
      810 Sqn. – 12 Swordfish
      818 Sqn. –   9 Swordfish
      820 Sqn. -   9 Swordfish
CL Sheffield
CL  Despatch
DD Faulknor
DD Firedrake
DD Forester
DD  Fury
DD Encounter
DD Duncan
DD Wishart
DD Kelvin
DD Jaguar

Force D
BB Ramilles
CA  Berwick
CL  Newcastle
CLAA  Coventry
DD  Defender
DD  Gallant
DD Greyhound
DD Griffin
DD Hereward

Force F
CL  Manchester
  Vice-Admiral L. E. Holland
CL  Southampton
DD  Hotspur

Note:  Source No. 2 refers to British Force B (Source No. 1) as Force H.

BB  Vittorio Veneto
   Vice-Admiral Inigo Camponi – Fleet Commander
BB Guilio Cesare

1st Cruiser Div., 2nd Sqn.
CA  Pola
   Vice-Adm. Angelo Iachino – Squadron Commander
CA  Fiume
   Admiral  Matteucci – Division Commander
CA Gorizia

3rd Cruiser Div.
CA Trieste
  Vice-Adm. Luigi Sansonetti – Division Commander
CA  Trento
CA  Bolzano

13th DD Flotilla
DD Granatiere
DD Fuciliere
DD Bersagliere
DD  Alpino

7th DD Flotilla
DD Freccia
DD Saetta
DD Dardo

9th DD Flotilla
DD Alfieri
DD Carducci
DD Gioberti
DD Oriani

12th DD Flotilla
DD  Lanciere
DD Ascari
DD Carabiniere
 

Sources:
1. Chronology of the War at Sea 1939-1945 by J. Rohwer & G. Hummelchen
2. The Naval War in the Mediterranean 1940-1943 by J. Greene & A. Massignani
3. The Italian Navy in WWII by A. Bragadin
4. Carrier Operations in WWII, Volume I: The Royal Navy by D. Brown