The following references should cover what you are after.
Britain: UK Statistical Digest of the War, also called Fighting with Figures, appendix 4 of British War Production by H M Postan, monthly production January 1938 to December 1944. National Archives file AIR 19/524, AIR 8/278, AVIA 46/146, AVIA 10/315, AVIA 49/229.
Royal Air Force Contract Cards and Delivery Logs.
Air Historical Branch/Archives. The Ministry of Aircraft Production (MAP) monthly Statistical Bulletin. The Ministry of Supply Monthly Statistical Bulletin.
The National Aerospace Library at Farnborough. Rate of attainment of peak output after first delivery, report no 5. 11/313.
United States. USAAF/USAF Statistical Digests.
U.S. National Archives RG (Record Group) 72 Entry 153 Boxes 1 and 2 USN Acceptances, RG 18 box 750 central decimal files 452.1 AAF Aircraft receipts 1939. RG 149B Entry C2743, U.S. Military Aircraft Acceptances 1940 - 1945 Aircraft, Engine and Propeller Production, U.S. Department of Commerce, Civil Aeronautics Administration. RG 179 Entry 1 Boxes 1086, 1087, 1089, 1092, 1094, 1096 and 1097, War Production Board Aircraft Reports, various months July 1940 to July 1945. RG 179 Entry 249B Box 719, Bulky central decimal files 452.1, Air Technical Services Command Special Historical Report of Airframe Weight 1940 to 1944.
AFHRA 218.8-2, Special Quarterly War Department Report on Airplanes, Material Division, Field Service Section, Wright Field, Dayton Ohio, Q1/1935 to Q4/1939. AFHRA 218.5, Materials Division, Operations Report on Airplanes, 1935 to 1939. AFHRA 134.23-8, Monthly US Aircraft Factory Acceptances and Deliveries, April to July 1943. AFHRA 134.23-16, Monthly US Aircraft Factory Acceptances and Deliveries.
USAF Material Command. Airplane and Glider Acceptances, Factory Deliveries and Departures from U.S, by type model and country, January 1940 - December 1942 inclusive. WS-301A/RC-301 (monthly reports).
Civil aviation figures and pre war military aircraft for export, the Aircraft Year Book by the Aeronautical Chamber of Commerce of America Inc (1936 to 1942) (Smithsonian Air and Space Museum Library, Washington). Statistical Handbook of Civil Aviation, U.S. Department of Commerce, Civil Aeronautics Administration, Washington D.C., December 1950 (Monthly figures 1945 to 1949) (US National Archives, College Park, Library). Department of Commerce, Supplement to the Survey of Current Business, 1936, 1938, 1940 and 1942, Statistical Supplement to the Survey of Current Business, 1947 and 1949, Business Statistics Statistical Supplement to the Survey of Current Business, 1951 and 1953.
Canada, Official munitions production of the United States by Months, July 1 1940 to August 31 1945, on microfilm 47369, Library of Congress, HD9743.U6 A58. (War Production Board Report). Also online.
Canadian National Archives, RG 24 Volume 5394 Monthly production report May 1944 to July 1946, RG 28 Volume 15 Aircraft Production History, RG 28 Volume 73 Aircraft Production Organisation, RG 28A Volume 39 Production reports July to December 1942, January to August and October and November 1943. Quarterly reports for Q2 and Q3 1942, Q1 and Q2 1943. Record Group 28 Volume 15. RAF Air Historical Branch, MAP Statistical bulletin March 1942 to September 1945 . British Archives AVIA 38/1029. Australian Archives. Series A1695 Control 3/101/Tech (3 parts), part 2, Canadian Aircraft Production March to September 1943, part 3, Canadian Aircraft Production September 1943 to August 1944 (available on the archives web site as an imaged document).
Australia: Australian Archives, Series A5954 control 225/5 Aircraft Production Report 1945, Series A5954 control 227/5, Aircraft Production Report, Beaufighter and Beaufort to August 1945 (it also includes cables of monthly production sent to the UK, US and Canada, mostly in 1942 and 1943). Series MP287/1 control 232, Commonwealth Aircraft Corporation Monthly Aircraft Production Reports. Series MP287/1 control 685, Monthly Aircraft Production Reports April 1941 to February 1943. Series MP287/1 control 685/1, Monthly Aircraft Production Reports March 1944 To May 1946. Series MP287/1 control 685/2, Monthly Aircraft Production Reports, June 1946 to August 1949. Series MP287/1 control 685/2A, Monthly Aircraft Production Reports September 1949 to March 1952. Series MP287/1 control 1186, Monthly Aircraft Production Reports, 1939 to 1941. Series MP450/1 control 83, Aircraft Production 1943. Series MP450/1 control 182, Monthly Aircraft Production Reports for 1939 to 1943.
Result, English speaking countries aircraft monthly production figures by factory, make and model, 1935 to 1949. Also engine production but not to the same detail. Factory names as per reports, Fairey can be Stockport or Errwood Park
Beaufighter | Fairey | Bristol | Bristol | Bristol | Fairy | Bristol |
Factory | Stockport | Filton | Filton | Weston | Stockport | Weston |
Mark | Ic | If | IIf | VIc | VIc | VIf |
Apr-42 | 7 | 19 | 29 | 17 | 20 | 44 |
Merlin April 1942. | | | | | | | | |
mark | X | XX | 21 | 30 | 45 | 46 | 60 | 62 |
No. | 101 | 977 | 18 | 41 | 164 | 249 | 15 | 3 |