In Locked Church Country

I was back in Kent yesterday, church crawling again - which isn't easy in a part of the county where the churches are all locked. Too quiet it is, and too near the main roads - once pilgrim routes, once Roman roads... But I struck lucky at one church when, after my mobile calls to two key holders proved abortive, I crossed the road to the rectory - as usual not The Rectory but a nondescript Sixties house hard by it - and found the rector by chance briefly at home between calls. She - again as usual a she: nice woman, friendly, northerner - took me back over the road, opened the church and left me to it. To a little gem of a church - plain white interior, chunky Norman nave with massive piers, later arcade to North chapel, chancel rejigged in 1689, as a boldly painted date over the arch declares. In the North chapel some beautiful stone carving, including a piscina set at an angle in a pier between chapel and chancel - and above the chapel altar the faded afterimage of a lovely, graceful Crucifixion group painted around 1300. And in the nave and chancel odd remnants of Baroque murals. And the main altar by Pugin the younger. And, displayed in a little wooden case, a mammoth's tooth - a tooth originally found by one of the builders of the Norman church and set in a pier near the font (also Pugin the younger) as a curiosity. Oh, the inexhaustible wonders of the English parish church...
 Heck, let's make this a competition: a prize of a punnet of finest Kent cherries* to the first person to Name That Church. Clue: it's quite close to this one.

[* subject to availability]