From what I can gather, her name may be Augusta Emma Hanover d'Este. The Estes were Hugenots who fled to England, but her father was Prince Augustus Frederick, son of King George III. She was given the d'Este name because her parents' marriage contravened the Royal Marriages Act of 1772 (superseded in 2013). The article about Augusta Emma Hanover d'Este in thepeerage is here.
From the Christie's Web site; image size doubled and made lighter by gogm.