IIRC it was the Poles who first started on Enigma well before the war and GCHQ built on their work - the special genius of the British as to build computing machines to speed up the decoding
And of course the British used women, gays, refugees, foreigners, Jews and all sorts of what the Germans labeled "undesirables" in the work - a whole pool of immense talent that was denied to the Germans due to ideology