The Wolseley helmet was around from at least 1896 - the start of the Sudan Campaign - but I have seen a photo of General Sir Gerald Graham, who led the campaign against Osman Digna in the Eastern Sudan 1884-1885, which shows him wearing at least a precursor to the Wolseley. His staff are all wearing the Colonial Pattern helmet (Zulu/Boer Wars etc.)

The Wolseley pattern was sealed in September 1899 and was first mentioned in the Dress Regulations, for officers only, in 1900 but only for the West African and Chinese Regiments. It was worn, unofficially, by officers in the Sudan and the 2nd Boer War but mostly by staff officers in the latter because of the accuracy of the Boer marksmen.

It was mandated for officers serving abroad in the 1904 DRs and spread to the army, as a whole, by 1910. The Wolseley, and its predecessor, the Colonial Pattern were supplemented by various sola pith helmets in the late 19th and well into the 20th Century. This was because of the cost of cork vs. sola pith and therefore the desire to make the cork Wolseleys last longer.