In the 1700s Southgate was not a parish but a chapelry of Edmonton, known as the Weld Chapel.
You’ll find the records on Ancestry, in the database London, England, Church of England Baptisms, Marriages and Burials, 1538-1812. To limit the search results, you can enter Southgate in the Keyword field
Or to read through the register by turning the pages, use the Browse panel on the right, selecting
Borough – Enfield
Parish – Weld Chapel, Southgate
Years – 1695-1812
You would probably be wise to consider entries for both Wadkins and Watkins, since there was little consistency in spelling at this date.