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Although a christening record has not been found for him Timothy Ley (Grimwade p.582) and Anna (nee Petley) who were married in 1684 at St James, Duke’s Place were probably his parents.
He married Cornelia Crawley at St Mildred, Poultry in 1711; he was from St Katherine Cree parish, Leadenhall Street. Three of their children were christened at St Katherine Cree from 1713-15.
He was assessed to Land Tax on unidentified property in Aldgate from 1713-1721. A new tenant was assessed in 1722.
In view of the unusual name the Will of Petley Ley, late of Deptford Stroud, Kent, proved for probate on 27th April 1757 may be relevant (National Archives reference PROB 11/829/435).

7 June 1717 Petley Ley goldsmith paid apprentice indenture duty for William son of Francis Larkin butcher.

To go along with Mike's opinion that there is a likely relevance to the Deptford will, the name of the wife mentioned in this document is Cornelia.

25 April 1689 Petley son of Timothy and Ann Lee birth recorded at Saint Gabriel Fenchurch City of London.

An example of the mark of Petley Ley: