I currently work in MOD Army kit supply.
The lanyard worn in the initial photograph is still worn by a number of regiments in the current (streamlined) british army with No 2 dress. It is white in colour & plaited for about 3/4 of the length. The lanyard was originally worn to carry items of kit, but is now purely decorative (apart from one or two regiments that wear whistles & the like on them; e.g. Rifles Band)
Off the top of my head the ones that wear the white lanyard are, Kings Royal Hussars, Scots Dragoon Guards, Queens Royal Lancers, Queens Dragoon Guards & Royal Dragoon Guards.
Royal Signals & Royal Engineers both wear a Navy Blue Lanyard but they are slightly different shades.
