Hello Helen - that's a good crop of confirming information. And very interesting to have W. E. Baxter's name there!
Providing he didn't have a middle name you're unaware of, I only see 1 London birth for an Alfred Wheeler - in Pancras, Jul-Sep quarter 1859. That possibly links up with the 1861 census family of Samuel Wheeler, a Police Sergeant - wife Sarah, siblings Oliver and Amelia.
There's also the bricklayer, John Wheeler (wife Frances - seems to be a Sarah in 1871) - son Alfred F. Wheeler b. Hammersmith - might be Alfred Frederick, b. Hammersmith 1858 from the birth index.
In 1881 the bricklayer family are still in London, including Alfred (also now a bricklayer). So is Samuel the policeman ... with Alfred Wheeler (now an unemployed iron moulder). This would almost certainly put them both out of the Afghan War ... though they could have been back in civvies by 1881, I suppose!
1891 - when Alfred, as William Campbell, was in the Cameronians - Samual Wheeler, Police Inspector is still around. I think his son Alfred is also still present - a piano forte finisher, b. St Pancras c.1859, married to a Jane. I can't find the bricklayer though (if he's still alive).