I have a final update regarding information received from the Sussex record office. They have in fact found several references to a John Athey in the Volunteer muster returns -
(1878) included Gunner J Athey of Brighton, no. 2407, enrolled on 2 April 1874. The return for 1874 confirmed this enrolment date and added his forename, John.
(1884) recorded him, initial only, as Corporal, with no. 2409, in No. 4 Battery, Brighton.
(1887) entered him as Sergeant J Athey, again no. 2409 in the same battery.
He passed his certificate of proficiency on 13 December 1884.
So given the confirmation that his forename was John, I think there’s no doubt that John William Athey, born 1850, is indeed the man in my photo. As you say, it’s great when things come together like this, so thanks for your help, it’s been really interesting.