I'm not entirely sure if this is the right place to ask this question as I know this is a very specific request; but from the limited sources I can find online I can't find any real details so I figured I would ask some experts.
My understanding of the situation is that in the Anglo-Zulu war in 1879 the British Army still mostly wore red tunics; but in the Sudan Campaign beginning in 1881, only a few years later they seem to be wearing grey or khaki.
At what point did this transition happen and how smoothly did it go? This seems to me like a very short time to issue an entire military with new kit, so were there any colonies around the world that were still wearing the red tunics at the outbreak of the Sudan Campaign? Additionally, what other changes were made apart from the colour?
Hey! So I tried twice to respond to your question on my phone. I failed both times. Hopefully the fates will smile on me now!
The British Army's foreign service dress in the latter part of the 19th century was essentially the same as that worn for home service. True, experimental issues of clothing had been made- notably, grey tweed Norfolk jackets, with brown cork sun helmets, and tweed or duck trousers worn by the troops in the 1872 Ashanti campaign. However, the only widespread deviation from home service dress was in India, where Khaki drill clothing was worn more or less universally after the Second Anglo-Afghan War (1878-1879).
The infantry dispatched from Britain and the Mediterranean garrisons to South Africa and to Egypt in 1881 still wore the five button scarlet serge frock, with facing colors on the collar and cuffs. The frock was worn with Oxford color trousers and black leggings, the only concession to the climate being the white foreign service helmet. This was frequently worn with a wound puggaree about the brim and dyed brown. Officers wore uniforms similar to the other ranks, their frocks, however, were privately made and tailored to their specifications. Cavalry wore frocks with pantaloons and either knee boots or putters. Opinions varied on the wearability of such woolen clothing, but it certainly made soldiers conspicuous targets in the field.
To compensate, frocks and trousers of grey serge were sent to Egypt, but arrived after hostilities had ceased. The garrison wore these uniforms, however, as did the troops on the Sudan Campaign and the Gordon Relief expedition. Notable wearers included the various Camel Corps, who wore grey serge frocks with cord pantaloons, blue puttees, foreign service helmets with wound puggarees and brown boots. The corps was equipped with brown bandoliers and waistbelts.
Khaki drill worn by troops sent from India proved more tolerable than Grey serge, and consequently frocks and trousers of khaki drilling were manufactured for use by the troops in Egypt in 1884, and saw use by the Guards brigade in the Suakin expedition of 1885. Khaki was worn by troops stationed on the Egyptian frontier to guard against Madhist incursions.
Scarlet had not yet seen its final days however. At the Battle of Ginnis in 1885, troops put on their scarlet serves to overawe the opposing Madhists. The dress of one battalion, the 1/Yorkshires, consisted of red frocks, blue trousers, putters and brown dyed foreign service helmets with puggarees. This was the last major action in which British troops wore scarlet.
Khaki drill became official dress in India in 1885, and was authorized as a foreign service dress in 1896, scarlet being retained for service dress at home. In 1902, Khaki serge became the service dress of the entire army, with the consequent abolition of undress.