Try looking in the Army List. There are some editions online and copies on the shelves in some big libraries, notably at the National Archives in Kew and the Society of Genealogists. The Army List only deals with officers, not Other Ranks. The Gazette can be really helpful but its search engine seems to be a bit hit and miss.
Where in Africa? At the outbreak of war, many settlers in British East Africa (which became Kenya) joined together to form ad hoc regiments which were later regularised. The campaign is not well known, being a bit of a side show to the Western Front, and has its own fascination. Try Tip and Run by Edward Paice.