Edmund Pleydell is traceable over the Internet because he was an MP. His article in thepeerage shows he had a daughter named Cornelia, but does not name his wife. There is no article in thepeerage for an Anne Luttrell.
From bbc.co.
Anne Luttrell wears the full van Dyck revival dress with lots of lace trimming in this Hudsonian portrait. There is a back panel suggesting she is wearing a robe à la française.
Keywords: Anne Luttrell, straight coiffure, hair jewelry, jeweled feathered hat, square neckline, chemise, neckline ruff, lace, full sleeves, bodice, strap sleeves, brooch, jeweled bodice ornament, jeweled arm bands, robe à la française