In the case of Deptford it was in part in Kent and the rest in Surrey.
West Kent Sources produced by North Kent FHS says 'Deptford ancient parish extended into Surrey. This part known as Hatcham became part of St Paul's in 1730 and a separate ecclesiastic parish in 1845.
The query arose for a record in 1770. In that case you need to look at all the parish registers as people moved across the boundaries.
St Nicholas parish registers from 1571 are at the LMA. Index only 1717-1769 at SOG.
St Paul's parish registers from 1730 are at the LMA.
The other parishes St John, Christ Church, St Luke, St Mark and Emmanuel are all 19th century churches and parishes.
Hope that helps anyone researching in that part of Kent. Local knowledge from family history societies is invaluable in situations such as this.