Greatcoat Cape, UK 1902-54; who wore it?

[ILH]

Hi all,
Took a small gamble on these two for £50, i think they are worth it, but I wasn't sure of the item on the left;

The ID of the blue Levee Dress Greatcoat Cape has me stumped. Garter order buttons with King's Crowns x4, black lining, no labels whatsoever:

Seller said it was for a Miltary Knight of Windsor (I don't think he is right)?
1901 regulations mention 3 and 5 button versions, but not 4. Also says black lining = Inspector of Military Schools?
Net came up with garter buttons for Royal Household Staff?
My dad (ex-Guards) reckoned it was a Royal Footman's?

Anyone know what it is- I would dearly like to nail this one?

Thanks,
Jim.

[The No.2 tunic is cold war, Ox & Bucks Light Infantry/ Green Jackets, with bullion S/Sgt and Para badges, named. The medal ribbons are Korea, Korea UN, GS Borneo, Kenya Mau-Mau, GS unknown, Cyprus UN, and LSGC.]