An alternate scenario that might work is this:
"The construction of the prototype began in March 1940, but work was cancelled again after the Battle of Dunkirk, when Lord Beaverbrook, as Minister of Aircraft Production, decided there was no production capacity for aircraft like the DH.98, which was not expected to be in service until early 1941. Lord Beaverbrook and the Air Staff ordered that production focus on five existing types, namely the Supermarine Spitfire, Hawker Hurricane, Vickers Wellington, Armstrong-Whitworth Whitley and the Bristol Blenheim. Work on the DH.98 prototype stopped; it seemed that the project would be shut down when the design team were denied the materials with which to build their prototype.
The Mosquito was given new life in July 1940, after de Havilland's General Manager L.C.L Murray, decided to transfer development to one of its subsidiaries in either Australia or Canada. With the de Havilland Canada already committed to production of DH.82 Tiger Moth trainer aircraft to support the British Commonwealth Air Training Plan, Australia was quickly chosen. This seemed a doubly prudent move given the impending fears of invasion in the UK. As it was, during the Battle of Britain, interruptions to normal production due to air raid warnings caused nearly a third of de Havilland's factory time to be lost.
In November 1941, the Australian de Havilland factory at Bankstown commenced production of the first Mosquito prototype. Initial delays were caused by the unavailability of Canadian birchwood, and Australian coachwood had to be substituted. The Australian team were greatly assisted by a contingent of British engineers and technicians led by Test Pilot Geoffrey de Havilland, Jr. The first aircraft would fly on 1st April 1941, with de Havilland himself at the controls,. This was an incredible achievement given the timeframe involved.
Initial production was split between RAF and RAAF requirements with the former receiving priority. The Air Ministry ordered 19 photo-reconnaissance (PR) models and 176 fighters. A further 50 were unspecified; in July 1941, the Air Ministry confirmed these would be unarmed fast bombers. By the end of January 1942, contracts had been awarded for 1,378 Mosquitos of all variants, including 20 T.III trainers and 334 FB.VI bombers..."
I will leave it to you to take further if you like...
