The sidcot suit is not a sheepskin jacket.
The 'Irvin' jacket is the sheepskin one, made by a number of contracts, most notably Irvin.
The Sidcot suit was developed by Frederick Sidney Cotton OBE (17 June 1894 – 13 February 1969) around 1917 time (IIRC). the pattern in use during the BoB was the 1930 pattern.
Not many fighter pilots wore either in the battle, although many wore the Irvin jacket during the BoF, and Bader notably wore the Sidcot suit.
Does Luthier need all this info? I sent Oleg pages of the stuff, and I detailed each specific item of kit available at the time
