Good morning,
Handcross is in Slaugham parish, the church is St Marys in Slaugham. There is also Staplefied Parish church, St Marks. Both are about a mile from Handcross and both have graveyards. Both have graveyard plans of burials in the porch There is also a Catholic church in Staplefield but no graveyard, have never heard of Staplefield Provident Chapel but will ask around. In Handcross High st is the Zoar Strict Baptist Chapel, no burial ground. If I see Pastor Bradstock I will ask about records, but the baptists do keep very good central records. There used to be another non-conformist chapel on the other side of the road but now demolished and don't recall what it was, again will ask around.
John915
The next nearest parish churches would be Balcombe, Cuckfield and Lower Beeding. I don't know what non-conformist chapels there were in those villages.