The Collection has commented: ‘We’ve been through the records and there is very little information about the provenance of this work. It did not appear in the 1898 Exhibition of Shropshire Antiquities and it is not in the donations books. It seems to appear on display at Shrewsbury Museum in the 1930s listed as "Judge Jefferies (?)". We suspect it belonged to the Shrewsbury Corporation in which case it would have been transferred to the museum without any record being made.’

This does not look like known portraits of George Jeffreys, 1st Baron Jeffreys of Wem, who was less than 45 years old when he died in 1689. Our sitter looks older, with a fuller face and rather more corpulent. See below;

https://bit.ly/3Tg5zKB

https://bit.ly/3PQM9Jp (said to be by John Riley)

https://bit.ly/3ApyQty

On page 149 of this book, a portrait of “Judge Jeffreys” at the "School Library" in Shrewsbury is mentioned.
https://tinyurl.com/yc3zhwmp

Mrs. Walford of Roden House, Wem, and the Rev. H. W. Moss, Headmaster of Shrewsbury School, lent portraits of Judge Jeffreys to the 1898 Exhibition of Shropshire Antiquities. See no. 37 on page 50 and no. 172 on page 62.
https://tinyurl.com/mr334v2t

The sitter, of course, is certainly wearing the robes of a judge, but the question is which judge.

At one time, a portrait of Judge Jeffreys was reportedly at Belswardyne Hall (Belswardine Hall) near Cressage, Shropshire. According to Google Maps, Cressage is 9.5 miles south-east of Shrewsbury.

Here is an extract from the 'Wellington Journal' of October 18, 1884, that provides more information about the portrait of Judge Jeffreys that was once at Belswardyne Hall.

The 1898 edition of ‘Bye-gones’ includes an image of one of the two portraits of Judge Jeffreys that were in the 1898 Exhibition of Shropshire Antiquities. Since the label indicates that the portrait was item #172, it would have been the portrait of Judge Jeffreys that was lent to the Exhibition by Rev. H. W. Moss, Headmaster of Shrewsbury School.

https://www.google.ca/books/edition/Bye_gones/INo4AQAAMAAJ?hl=en&gbpv=0

It’s very doubtful that this is a portrait of George Jeffreys, 1st Baron Jeffreys of Wem, known as Judge Jeffreys, as Jacinto has already pointed out (25/08/2022).

In answer to the discussion question, “Who might have painted this portrait of Judge Jeffreys?”, I’d suggest the following:

SITTER: Not Jeffreys. The collection suggests that this portrait may have come from Shrewsbury Corporation. A diligent search of the Corporation’s records may throw light on the portrait. Otherwise it will be difficult to identify which judge is depicted.

ARTIST: Martin asks, “Could this be a provincial copy of a painting of the stature of John Riley?” (25 Aug 2022). This could be the case. Alternatively the artist may have used an engraving of a portrait of some judge or other by Riley or another artist as the basis for his painting, just altering the head.

I am not a fashion expert, but the wig looks later than 1670s, more like 1690-1710.

The similarity may well be moot, but see https://bit.ly/3tKke52

However, if our sitter was a Baron of the Exchequer, he might be Sir Littleton Powys https://bit.ly/3EiYT7P from Shropshire. A portrait of him at the Tarlton Law Library at the University of Texas (Austin) may be our man at a younger age; see https://bit.ly/3EKIqdZ

As noted above, this is more likely to be Sir Littleton Powys than Judge Jeffreys, though Powys remains possible but not certain (his brother, Sir Thomas Powys https://bit.ly/42wMSGO, was also a judge). I would suggest calling this "Portrait of an Unknown Judge" and perhaps adding a note to the Art UK entry like "It has been suggested this might be Sir Littleton Powys (1647-1732), a judge from Shropshire, whose brother Sir Thomas Powys was also a judge."