What a find! In the London Metropolitan Archives I have found a document where John Benjamin Tolkien (1752–1819) is presented as "a Native of Dantzic"! This is the first document from London in my collection where J. R. R. Tolkien's great-great-grandfather is described as a person coming to England from Poland! The document comes from April 1813 and is a petition of John Benjamin Tolkien (1788–1859), son of John Benjamin Tolkien (1752–1819) to be admited to the Freedom of this City [of London]. The only problem is that in this document John Benjamin, the father, "came to England about the year 1752 when he married a Native of this Country and has resided here ever since and where your Petitioner was born".
We know that John Banjamin Tolkien came to England after 1770 (where his older brother Daniel Gottlieb Tolkien came to London from Danzig via Amsterdam) and that he married a native of England Mary Warner in 1777 (see my text about John Benjamin Tolkien here). Maybe his son wanted to have deeper English ancestry and his "about 1752" meant the same as "about 1770"?
Source: Ancestry.com. London, England, Freedom of the City Admission Papers, 1681-1930 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010. Original data: Freedom admissions papers, 1681 – 1930. London, England: London Metropolitan Archives. COL/CHD/FR/02. London Metropolitan Archives