No, this was not a factory car:(From a bit of net surfing) By only unique you mean the factory car right? Looks like they were late to the party in 64. What's wrong with privateer cars?.. Protheroe's looks much nicer without those second headlights Either would be a very welcome addition IMO.
http://www.myitshere.co.uk/DProtheroe/e_cut7/ec1001.htm
https://www.classic-motor-cars.co.uk/lindner-nocker-lightweight-restoration_28
https://fr.wikipedia.org/wiki/Peter_Lindner
https://www.ultimatecarpage.com/txt/2326/2/Jaguar-E-Type-Lightweight-Low-Drag-Coupe.html
There are NOW multiple reproductions of it but at the time, it was unique although other light weigh low drag were built.
https://www.bonhams.com/auctions/20145/lot/155/
https://www.goodwood.com/grrc/race/historic/2015/2/goodwood-greats-jaguar-e-type-low-drag/