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In All Saints' Church, Kingston Seymour, Somerset. His birth would seem to have been registered in the second quarter of 1873, making his age at death 27, not 28.
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Although resident in Brighton, his name doesn't appear to be on a memorial there.
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....DEATH OF A RESERVIST.—The death is announced from South Africa of 3,076 Private S. Hale, 2nd Grenadier Guards, son of Mr James Hale, and nephew of Mrs Sarah Payne, both of this parish. The deceased, who was a reservist, succumbed to an attack of enteric fever at Leribe on Friday, the 19th inst. Previous to his departure for the seat of war he resided at Brighton, where he leaves a widow and two children, for whom much sympathy is felt to mourn his loss.
The Clevedon Mercury and Courier, 27th October 1900
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....“There was a large attendance at the church on Sunday afternoon, at the unveiling of the tablet to the memory of Sydney John Hale of the Grenadier Guards, who lost his life in Africa. Special hymns were sung at the service, at which the Rev Preb. H. Vaughan, R.D., gave an address. Colonel W. Long, C.M.G., unveiled the tablet, which is in the form of a marble shield, set in Mangotsfield red stone, with the crest of the Grenadier Guards in alabaster. The 2nd Wessex Royal Engineers (Clevedon and Weston), under Captain J. F. Keen, Captain Fry, Lieutenants Lockett and Butterill, were present. Headed by their brass and fife and drum bands, they afterwards marched back to the railway, and were entertained to tea at the coffee house by Mrs Livingstone Ogilvy, the lady who had the memorial erected.
Western Daily Press, Monday 5th October 1908

Pres Brand Cemetery, Bloemfontein

British Memorial

Fantastic research Berenice and Elmarie. Many thanks

"marched back to the railway" presumably means they marched to Yatton railway station, that being the nearest station to Kingston Seymour, and trains ran to both Clevedon and Weston-super-Mare from Yatton. There's a Railway Inn at Yatton, but the report says they went to a coffee house.

Mrs Annie Isabella Livingstone Ogilvy (c.1851-1924) was also connected with the ABW peace memorial (1903) at Clevedon, on which Sydney Hale (as Sidney) is named.