Roy Precious - Antiques & Fine Art has dated this piece to the 17th Century.
Interestingly they did not name the sitter and they gave Sir Peter Lely as the artist. I am reluctant to challenge a Spink attribution, but I believe 'Studio of Lely' is more realistic.

(Our thanks to the art dealer and historian Peter Harrison of Harrison Fine Art who spotted this ad in the Witt Archive.)
The attractive young sitter has long been known as Betty Fitzwarren; there is a strong possibility that she was born Lady Elizabeth Bourchier in 1622, died 22 Sept 1670, eldest daughter of 4th Earl of Bath, of Tawstock, Devon

She married (8 July, 1641), as his third wife, Basil Feilding, 2nd Earl of Denbigh, of Newnham Paddox, Warwickshire.
As her husband attempted to navigate the treacherous waters of Civil War and Restoration, she wrote him numerous letters which survive (some transcribed in the book "Royalist Father & Roundhead Son", the full text of which can be found on the internet), and include passionate postscripts such as "a hundred thousand thousand kisses I give thee" and "Dear! how thy Betty loves thee!" The book also describes the elaborate arrangements made by the Earl for her funeral.

Backtracking slightly, her father had died in 1637, leaving Elizabeth and her two sisters, but no sons; so a cousin became the 5th Earl and it was no doubt he and his wife (Lady Rachel Fane) who looked after the three girls and secured for them advantageous marriages (an Earl apiece). Interestingly the household accounts of the Earl and Countess for the period from 1637 survive and record numerous payments for portraits made to Geldorp, Van Dyck and Lely [see Wikipedia entry for 5th Earl of Bath].

The 4th Earl was also Lord Fitzwarren, a subsidiary title of great antiquity created in 1295 for Fulk FitzWarin, a Marcher Lord from Oswestry. Unlike later titles, ancient baronies created by writ descend by cognatic primogeniture, such that this prestigious title did not pass with the Earldom but remained vested in the three daughters and their heirs. It seems a strong possibility that Elizabeth might be referred to as "Betty Fitzwarren"...the affectionate diminutive was much in vogue at the time.

SIR PETER LELY (1618 - 1680) was the most important portraitist in the reign of Charles ll, although he had painted portraits throughout the Commonwealth. Principal Painter to the King, he painted everyone of importance, maintaining a busy and active Studio to help with the huge demand for his portraits. Members of his Studio, many of them talented artists in their own right, emulated his style to supply this constant market.
SIZE: 37.5 x 32 x 2.25 inches including the frame.
PROVENANCE: In 1937 with the eminent dealers Spink.
Australian Private Collection for a number of years.
Roy Precious - Antiques & Fine Art has dated this piece to the 17th Century.
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