Re. your great grandfathers burial at Budbrooke.
Are you aware that there is a public cemetery about 1 1/2 miles from the hospital, as you travel into Warwick? I think this cemetery is probably within the confines of the parish of Budbrooke, which lies between Hatton and Warwick.
Is it possible that, when burials ceased to be held within the hospital grounds, patients were laid to rest in this cemetery?
Just a suggestion, but might be worth your while to check it out.