They did, it was called the Spitfire MkIX and then the Mustang Mk III. The Spitfire was used to assist the USA until well into 1944. Mustang MkIIIs (P-51Bs) were assigned to the British before the USA settled on using the P-51Bs as a bomber escort themselves, so one of the jobs Hap Arnold had was to ask the British to use their Mustang IIIs on US raids. It was of course a rhetorical question, but it was done. Having a two stage Merlin available in 1942 doesnt mean you can commence mass raids. As far as I remember there were 6 squadrons of Spitfire Mk IXs operational at Dieppe (Aug 1942) The P-51 B started being produced in mid 1943 but there were only 100 in UK squadron service for big week Feb 1944.Again, nice thought but even though the Spitfire IX had the performance, it didn't have the range. The Spitfire was designed around a 500 mile or so range when it was first designed, and in terms of actual combat, never really got much better. Even the Griffon Spitfires only had enough fuel increases to keep the range to about 500 miles on typical combat missions.
So I ask the question: if the RAF wanted it, and by 1942 it was viable, why didn't they pursue it? Again, it almost seems that they didn't think a domestically produced aircraft of that type was viable, either though concept or being able to be built in England, or even if it was thought possible, no one was readily available to make it or design it.
In fairness to Britain, they did have smaller land mass than the US, less raw materials, fewer factories and a smaller population vs say the US. So that was probably part of the issue (industrial infrastructure). Of course, hindsight being 20/20, even in England there were underworked companies or those that were producing designs that weren't picked up (Boulton Paul, Westland, Airspeed, etc), but even those companies were also doing important subcontractor work for the RAF and RN.
It's almost like the Heinkel He-100 thread. It did, in altered form, almost make it into production. But in much modified form, and you'd have to wait for the Junkers Jumo 213 and Daimler-Benz DB603 engines to be produced in quantity That wasn't until 1944, and by then other designs and such took priority over the Heinkel P.1076..