No, the "Universal" wing started life as the "C" armament, since it could take 8 x .303", or 4 x 20mm + 4 x .303", without too much effort. The E wing was a conversion of the universal wing, but was not able to be converted by just anyone, since it involved the removal of a lot of pipework, and couldn't be converted back.
The E wing was 1 x 20mm + 1 x .5", full stop; it did not find favour with the Air Ministry until early 1944, when the gyro gunsight became available; until that time, the "brass hats" preferred to stick to the 4 x .303" with the 2 x 20mm, since the extra number of rounds meant that there was an even chance that the average pilot (who struggled with deflection shooting) might actually hit something. Once the new sight appeared, skill levels rocketed; the .5" was also better for ground attack, hence the XVIe F.R.XIVe.
The E wing was never designed to take 4 x 20mm; that armament didn't arrive until the new wing, of the 20-series, made its appearance.
The C wing was not designed to take the .5", either, though there are stories of the Canadians shoehorning them into some of their aircraft. Being a much bigger item, the .5" would never have fitted into the outer m/g compartments, and, on the IX, the outer "cannon compartment" was, in fact, taken up by the pipework taking hot air, from the radiators, out to the outer .303"s..