Ah, the PDF search can be a bit weird on French documents, so I checked the Index of St. Jean, Spitalfields 1687-1827 and came up with:
FIELD. 1732, 3 Sept. Guilliaume, f. de Thomas, et d'Anne Ardelay; bap. par Mr. J.
d'Agneaux, Min. du St. Ev. P. Le pere. M. Magdellaine Jardelay. Ne 16 Aout
Could Guilliaume be your William?
Also three other children of Thomas & Anne:
FIELD. 1734, 15 Sept. David, f. de Thomas, et d'Anne Hardeley; bap. par Mr. J.
Barnouin, Past. P. Daniel David Pontardant. M. Marie Hardeley. N£ 24 Aout.
FIELD. 1738, II Juin. Thomas, f. de Thomas, et d'Anne Hardeley; bap. par Mr. J.
Manuel, Past. P. Nicholas I'Heureux. M. Anne Samson. Ne 26 Mai
FIELD. 1743, 28 Nov. Thomas, f. de Thomas, et d'Anne Hardeley; bap. par Mr. P.
Masson, Past. P. Le pere. M. La mere. Ne 9 Nov
So I may have been a little hasty saying that he was definitely not a Huguenot. This doesn't necessarily mean that he was, but he could have been.