The council run Llantwit cemetery is on the opposite side of the road to the older Church cemetery on Neath Rd. The council would only have details of burials in its cemetery (i'e. not the Church section). I can tell you that having visited the Vicar a number of years ago to see the Church burial registers (weren't on line then), there is no cemetery plan and so looking for a grave is pot luck, especially in the older overgrown part.