HiWhat about go whole hog and have the Brits build their own R-2800 under license and Hawker or Gloster or Boulton Pall or Morris Motors or whoever build P-47's. You get a lot better airplane than a Typhoon, one that will not terrify its pilots about crossing the Channel and leave British industry free to pursue jets. After all even the Tempest did not last after WW2 and the Sea Fury did not have a long life, because of the jets.
The trouble is with building P-47s is that they would have been very late war aircraft. The P-47 first flying on 6 May 1941 (and had its own developmental problems including with the engine, all of that would have to have been sorted out before any license production in the UK), the first Typhoon production machine flying 17 May 1941 (first P-47 production machine in March 1942). By the time the P-47 undertook its first operational missions with the US 8th AF from 13 April 1943 the Typhoon had been shooting down low level raiders and had undertook day and night ground attacks over France, despite its problems, for a year or so. So unless Republic could have got the P-47 operational a year or so earlier it was a non-runner for being a Typhoon replacement, your suggestion would just have been another "too little, too late" in WW2.
Mike