Doesn't look like an RA badge. I'd say it was a Yeomanry regiment.
Difficult to tell exact shape/size of cap badge, but something like the Dorset Yeo., or the City of London Yeo. look possibles.....
Do a web search on; "yeomanry ww1 badge" and see what else looks likely.
Also, try here on Donald's name & "yeomanry" in the Mil. section