100 octane was a fairly new idea for the Brits at the time (so to speak). I don't think it could be instantly distributed and every engine up-rated for its use so fast. Logistics takes time.
The process of switching to 100 octane began with tests and order for the fuel in 1937, by November 1940 (just as the battle finished) the stockpile was 500,000 tons.
There are various air ministry documents recommending the immediate switch over dating from late 1939, and the technical documents show that it wasn't a very complicated procedure.
In fact, switching to CS props was probably more complex, and the entire Spitfire and Hurricane force was converted in very short order (1 - 2 months)
From my understanding the 100 octane was in short supply AND was being stockpiled for use with upgraded spitfire engines, but was not yet widely dispersed, nor widely used.
Apart from the size of the stockpile, Mike Williams has now documented 18 Spitfire squadrons running on 100 octane during the battle, which is pretty much all of them.
Wood and Dempster note that FC used 22,000 tons of 100 octane between July and October, which is enough for about 6000 Spit and Hurricane sorties a week, the actual total of operational sorties was about 4,000 a week.