Hello,
not sure if this will help but, before ww1, the Royal Horse Artillary had what was in effect a 'pals batt' based in Blackburn/Clitheroe which was known locally as the Northern Horse. This was in effect a T.A.or home guard unit.
It was reconstituted in 1920 as the East Lancs brigade R.F.A. with 2 east lancs batteries and two cumberland batteries (the horse) Its headquarters were in Church.
In 1921 it was redesignated the 51st East Lancashire and
Cumberland Brigade which by then included units of the westmorland yeomanry.
In 1924 in was again redesignated 93 East Lancs Army Field Brigade and no further mention of horse.
I can find no unit deployments for India in the times you gave, but that is not surprising as they list no scale unit movements between the 1916 Gallipoli campaign and the 1939 B.E.F. in France.
What might be of interest though is the fact that in the very early parts of ww2, a number of indian units were attached to them, mainly in North Africa and it is not inconcievable to think that these may have been continuing arrangements from between the wars.
As said earlier, not sure if any of this helps but if it does I have further information on this unit and its history should you need it. Good luck in your search
Pat