Hence my proposal of and aircraft that was essentially "half a Hornet", since it would be single seat, single engine, have sufficient range, and for sure (even with a Merlin 60 series engine instead of the 130 designed for the Hornet) would have the speed and agility required, and might be as good as, if not better, than the mass produced Merlin Mustangs (not counting the P-51H). Also, de Havilland and their design team did show that "thinking outside the box" concept with the Mosquito, Vampire and Hornet.
However, if they were to design such a fighter, there would've been basically only a brief period of time for them to have done so from late 1941-early 1942. Since this is a hypothetical thread, lets take the DH example. In that period stated, they were being under utilized by the RAF, meaning they did have design, R&D and maybe some production to spare. That, however, if we look at the realities, rapidly changed in early 1942. The Mosquito would quickly come into huge demand once it entered service in it's recon, bomber, heavy fighter and night fighter roles. The RAF and the Air Ministry took the project for a jet fighter that would yield the Vampire a lot more seriously. And even though de Havilland would drop the DH.102 project (for a medium bomber that was basically a slightly enlarged Mosquito), it would be resurrected as the DH.103 (Hornet) long range fighter project. And even though that didn't gather a ton of interest from the Air Ministry at first, the expansion of British action outside of the CBI theater in the Pacific Theater would make the Hornet very appealing.
Hence, you can maybe say that if the Hornet was prioritized earlier, the British would've had their own equivalent to the P-38 in both Europe and the the Pacific. But though the Hornet is a single seater, it's twin engine so doesn't really fit in here as such.
And the problem with Miles and Folland is that though they did produce good designs if they were given a chance, it seems that the Air Ministry didn't take those designs seriously, or looked at the size of those companies and judged them as too small to make the numbers required if adopted. Not to mention that those companies did also fill niches that others couldn't due to being back-logged. Martin-Baker, for example, made seats, cannon feed systems, and ultimately developed the modern incarnations of the ejection seat. And Miles still made trainers and light aircraft for the RAF and Royal Navy. Of course, these are interesting "what could've been" items themselves.