Anne Cullum, née Berkeley, Lady Cullum by Olive Munro (St Edmundsbury Museums - St Edmundsbury, Suffolk UK)
Her article in thepeerage adds she was the daughter of Christiana Riccard. While her birth date is unknown, she had younger siblings born in 1662 and 1663. The Kniller (Kneller) brothers arrived in England in 1674. Kneller's Wikipedia article states, "He founded a studio which churned out portraits on an almost industrial scale, relying on a brief sketch of the face with details added to a formulaic model."
From bbc.co; spots removed from background with Photoshop by gogm.