Who was Miss Elizabeth Hamilton?

I recently read a reference in The Polar Star (1829: 79) that would be a significant historical discovery indeed. Quoted verbatim, this was the claim:

"The 'Cottagers of Glenburnie.' Ah! By the late Mrs. Elizabeth Hamilton? By the way, among Mrs. Hamilton's papers are some curious letters from Mr. Pitt. How is it her executors do not give them to the world? The late Bishop of Winchester [George Pretyman-Tomline, Pitt's own executor] was once heard to say that if Mr. Pitt had ever married, the lady would have been Miss Elizabeth Hamilton. And this I can most fearlessly assert of one letter in particular, that if it had been written by any common, every-day man - any one, in fact, but a prime minister - it would have been, by common mortals, unhesitatingly pronounced a love letter."

From the mention of The Cottagers of Glenburnie in the snippet, I presume that the particular Elizabeth Hamilton being referred to was the Scottish writer and educationalist (1757-1816). It is possible, however, that the Bishop of Winchester meant another Elizabeth Hamilton. 

If anyone reading this post knows where Elizabeth Hamilton's papers are deposited, or has any further information regarding the whereabouts of such letters - if they are still in existence - please do get in touch with me. Until this can be confirmed by concrete evidence, it is impossible to give credit to this statement.



Reference:

The Polar Star, Vol. 1. (1829) London: H. Flower, p. 79.