I too am a descendent of William Brinton and Ann Bagley, and sad to say-- the royal lineage of Ann Bagley is the subject of much dispute.It appears that we cannot claim this royal lineage without resolving this dispute, which in my opinion will NEVER be resolved as the necessary documentation does not appear to exist.
Some of this was sent to me via e-mail, and some I found on the medievel newsgroup of Usenet.
Ann Sutton's Lineage appears to be in dispute as follows:
 Donald Yoder, in Quaker Sketches (Chicago, 1942) stated that John Bagley's wife was a daughter of Edward Sutton, 6th Lord Dudley, without evidence.
In a series of letters published in THE PLANTAGENET CONNECTION (April 1995), pp. 18-22, various theories are discussed by Leslie R. Tucker, Charles Hansen and Neil Thompson.
Tucker thinks it clear that John Bagley's wife was the daughter of Edward Sutton and Elizabeth Tomlinson, primarily because John's sons were left substantial sums in her wills.
Hansen refers to Dudley Dudley's certification of the Visitation of Dudley, 10 April 1663, in which he refers to himself as the eldest son of this couple, and lists six sisters, five of whom were married to others than John, and the last having died young. He opines that John Bagley's service to Edward, Lord Dudley, as his principal deer keeper, was the motivation, and explains the name pattern as perhaps evidence of a godfather status to those named Edward and Dudley. He believes there is no direct evidence of descent from Edward Sutton to John Bagley's children, but suggests his children could be the sons of a daughter of Lord Dudley by another mistress.
Neil Thompson says "there are some suggestive things about the proposed connection, but that is far from being proved... the wife of John Bagley cannot have been a daughter of Elizabeth Tomlinson, even though she may have been a daughter of Lord Dudley".
The "editorial conclusion" following this exchange states:
"The expert opinion at this time seems to believe that the unknown woman who was the wife of John Bagley was still an illegitimate daughter of Lord Dudley, though probably not Elizabeth Tomlinson's daughter. Proof of this seems to be clear from the list of siblings of Dudley Bagley at the Visitation. Yet the naming patterns, the land leases, the substantial financial bequests provide good circumstantial evidence that John Bagley's children by his unknown wife were still grandchildren of Lord Dudley. If their grandmother was not Elizabeth Tomlinson, then she may well have been another mistress of Lord Dudley, another unknown woman who shared his life and bed prior to Elizabeth Tomlinson, and probably before his marriage to his legitimate wife, Theodosia Harrington. If this is so, then the line still proceeds to the royal houses, but still must be regarded as circumstantial and not proven evidence.
The conjecture that Lord Dudley may have been a god-father seems highly remote, as does the possibility that John Bagley's children were rewarded for service to Lord Dudley by their father.... After all this time, the line will probably never be proven beyond doubt, but the likelihood that the line continues to Edward III and beyond seems to be an acceptable hypothesis.
Our view is that this lineage should be included in collections of royal descent with a disclaiming commentary on the probability of the connection".
Hansen provided evidence to show there was no descent from the Suttons in The American Genealogist, Vol. 71, No. 1 (January 1996) in his article "The Ancestry of William and Ann (Bagley) Brinton: Quaker Immigrants to Pennsylvania", pp. 36-48.
As evidence for the fact that John Bagley's wife was the sister of Elizabeth Tomlinson (and thus the bequests to her sons) he notes the administration of the will of Elizabeth Tomlinson filed in the Prerogative Court of Canterbury was given to "Edward Bagley, nepeti ex sister" of Elizabeth.
The given name of John Bagley's wife is not proven, although it is possible that she was Agnes Tomlinson, who for present is listed as a sibling whose baptism is of record.
Those of us who share Hugh Harry or Ann Bagley as ancestors have read that these two persons connect us to the royal families of Europe. Recent research has indicated these claims do not appear to be well supported.
Thomas A. Glenn, in Welsh Founders of America (1911), Vol. 1, at pages 136-38, correctly gives Harry Thomas Owen of Machynlleth, Montgomershire, Wales, as the father of Hugh Harry (or Harris as it is sometimes reported). From that point he went on to construct a royal lineage. But "Hugh Harry, Quaker Immigrant to Pennsylvania", a 1994 article in The American Genealogist, Vol. 69, pages 95-97, by Neil Thompson, provides convincing evidence that Harry Thomas Owen was not the son of Thomas Owen , son of Rowland Owen, Sheriff of Montgomershire in 1611, and descendant of royalty.
Likewise, it has been stated that Ann Bagley, the daughter of Edward Bagley, and granddaughter of John Bagley, was descended from royalty as John was married to a daughter of Edward Sutton, 8th Lord Dudley. It had been believed that this daughter was born to Elizabeth Tomlinson, Edward Sutton's mistress.
A series of letters in The Plantagenet Connection (April 1995, pages 18-22) provided differing views of this possible relationship, and the editors concluded there was a basis to believe Ann's grandmother was perhaps a daughter of Edward Sutton, but by an unknown mistress rather than by Elizabeth Tomlinson.
Charles Hansen's article "The Ancestry of William and Ann (Bagley) Brinton: Quaker Immigrants to Pennsylvania" in the January, 1996 issue of The American Genealogist, at pages 36-48, provides convincing evidence that Ann's grandmother was a sister of Elizabeth Tomlinson (explaining the connection to the estate of Edward Sutton) rather than Sutton's daughter.
Given the above controversy surrounding the validity of this line, it is highly probable that we may NEVER know the truth about Ann's parentage.