|The newly-wed Lady Harriot Eliot's signature on her letter to Lord Eliot|
After the wedding, Edward and Lady Harriot went to live for a time at Putney Heath, perhaps at the former rented property Pitt occupied until he purchased Holwood in 1785. Eliot's town residence was at Spring Gardens, a place that was not far from Pitt's Downing Street.
There is a letter addressed to Edward's father, Lord Eliot, from Lady Harriot Eliot, which was sent from Putney Heath. Although undated, it would have been written between September 1785 and September 1786, as Lady Harriot sadly died in childbed only a year after her marriage.
It seems the newly-wed had not yet met her father in-law, and had recently heard he was coming to visit them:
"My Hond. Lord
It was with ye greatest pleasure I Learnt from Mr. Eliot Yesterday that you was so good as to think of making us a visit at Putney; but I am really so very earnestly desirous to assure you, at ye earliest moment I can, of my Duty and Respect, that I cannot help venturing to make it my earnest request to you to be allowed ye Happiness of being introduced to you to morrow at Spring Gardens [Eliot's town residence], and I will wait upon you at any Hour that is most agreeable to you. Permit me in ye mean time to assure you that I am with great Regard,
My Hond Lord,
Your Obedt. Humble Servant and Dutiful Daughter,
Putney Heath Wednesday morning." 
It appears Lady Harriot preferred to meet her father in-law in Town. I hope the introduction went smoothly!
1. Lady Harriot Eliot to Lord Eliot. Cornwall Record Office, Eliot Papers: EL/B/3/4/30.
The newly-wed Lady Harriot Eliot's signature at the bottom of her letter to her father in-law, Lord Eliot (same reference as above).