Hi Lesley,
Well first of all, the RHA is his regiment! In fact the RHA was part of the Royal Artillery along with the Royal Field Artillery (RFA) and the Royal Garrison Artillery (RGA)
You might find the RA museum site of interest
http://www.firepower.org.uk/index.phpThe best starting place to look for anyone you suspect may have been in the Boer War is the QSA (Queens South Africa) medal rolls. All British soldiers serving in South Africa at the time were entitled to receive this medal.
I have the QSA rolls for the artillery and I think I've probably found your man. There can't be many men with that surname which is why I'm fairly confident.
72269 Gunner A.Puxty, R-Battery, RHA
Received the medal with 5 clasps for Relief of Kimberley, Paardeberg, Johannesburg, Diamond Hill, Wittebergen
http://www.northeastmedals.co.uk/britishguide/queens_south_a...