I found several Goldsmith works that might reasonably be referred to by the title “The History of England”, all in the list of selected works of Goldsmith, with links, at http://bit.ly/2sMBINo:

• An History of England in a Series of Letters from a Nobleman to His Son (1764);
• The history of England: from the Earliest Times to the Death of George II (1771); and
• Dr. Goldsmith’s History of England, Abridged by Himself, to which is added a very Extensive and Faithful Continuation to the Death of the Duke of York (1774).

I looked in the second of these for this quote without success. Then I discovered the first and found the quote therein. It’s in Letter I on p. 3, not in any introduction. You have the correct publication date, but my searching indicates that “The History of England” almost always refers to the second of these three titles.

Just for fun, I also learned that there is also “Pinnock’s improved edition of Dr Goldsmith’s abridgment of the History of England with a Continuation to the Reign of Terror of George the Fourth” (1821?) and even “Whittaker’s improved edition of Pinnock’s Goldsmith’s History of England, from the invasion of Julius Cæsar to the death of George II, with a continuation to the present time” (no later than 1843). I didn’t look to see the relationship of these to Goldsmith’s original works.