One of the other main deciding factors for British aircraft production was engines - they couldn't produce enough of them.
Airframes were never really an issue, all wartime aircraft were disposable, so the use of semi-/quasi-skilled labour & less than perfect materials wasn't a problem (the dH Mosquito is a perfect example) &, if you could set up a few jigs & run a welder & pop rivets, you could make them in any old barn.
Engines, on the other hand, had precision tolerances, ran at high speeds & high temperatures, with high stresses & needed to be as light as possible. These required highly skilled labour, high quality materials & precision engineering.
In this case the Bristol
Perseus engine had, also, almost reached the peak of its development (the final Mk's did develop 1,200 hp). Bristol & the government would have wanted the focus to be on the
Hercules &
Centaurus engines, which had much more development potential (just as they had curtailed the production of the RR
Peregrine, which was the culmination of old technology, in favour of the
Merlin).
If you look at the list of aircraft the
Perseus was used on you'll note that none of them were really contemporaries of the Flamingo, with the exceptions or the Roc, Skua & Lysander. The Roc & Skua were 2nd rate aircraft indicative of Britain's poor grasp of the importance of naval air power in the war to come (focused as they were on the "War in Europe" scenario) & which they saw as unimportant, until they lost everything north of Malta & began a mad scramble to rectify their oversight. The Lysander was a special case & didn't need a great deal of power &, even so, the
Perseus was only used in the Mk.II version.
Blackburn Botha
Blackburn Roc
Blackburn Skua
Bristol Bulldog
Bristol Type 148
Cunliffe-Owen Flying Wing
de Havilland Flamingo
de Havilland Hertfordshire
Gloster Goring
Hawker Hart
Saro A.33
Short Empire
Short Scylla
Vickers Vellox
Vickers Vildebeest Mk.IV
Westland Lysander Mk.II
Still, with a different engine & with a time-line twist, you could probably get away with it.