Only eventually.
In 1940, Britain produced 15,049 aircraft, compared to 10,826 for Germany, 10,565 for the USSR and 6,086 for the USA. In the early stages of the conflict, such as during the Battle of Britain, Britain (which many people forget was an industrial superpower at the time) was producing almost as many aircraft as the USSR and USA COMBINED. This stunned the Krauts, who seriously underestimated the scale of British aircraft production during the Battle of Britain.
During WWII, Britain produced 131,549 aircraft and the USA built 297,199. At the time, the USA had three times the population of Britain yet produced just twice the number of aircraft. When taking population into account and the number of workers in each country, Britain was far more productive than the US.
https://en.wikipedia.org/wiki/Military_production_during_World_War_II#Air_forces