Seems like Grumman Martlet I should be entered as an option since it began arriving in Britain in the late Summer of 1940 and by October, 12 units equipped 804 squadron. Battle of Britain duration taken as: 10 July to 31 October, 1940, although the Martlet didn't score until December.
According to wikipedia, Martlet I is the only US produced fighter to be officially listed as equipping a BoB Squadron:
Perhaps if FAA/RAF/BPC had had a crystal ball, it's perhaps just possible it could have been flown in combat by late Summer or early Fall, if pilots had been given training in type in the states virtually as they rolled off the production line. Crystal balls were in short supply however, and such expediencies as stateside pilot training probably lay about a year in the future.
I've been told by old timers at Lockheed (when I worked there in the 1980s) that the Anglo-French Purchasing Committee order kept the P-38 line open and in fact the British never intended to purchase the P-38 for both performance and political reasons. In the end the British order was taken over by the USAAF after Pearl Harbor