Based on Patricia L. Hatcher's article "Identifyng Judith Hone, wife of John Armistead of Virginia ..." in the 2012 _American Ancestors Journal_, Gary Roberts includes a somewhat speculative royal line through Browne of Tolethorpe, co. Rutland, for these Virginia families. The line goes, in part, ...
Grace Pinchbeck = Christopher Browne of Tolethorpe
Francis Browne = Margaret Mathew
Joan Browne = William Hone
Thomas Hone = Jane Allen, etc.
This is based on the Visitation of Essex account of the Hone family, which states the connection to Browne of Tolethorpe, as well as the will of William Hone, in which is named his "brother" Anthony Browne. There is also a marriage record for William Hone and Joan Browne, as mentioned by Hatcher. The 1681 Visitation of Rutland supplies the earlier generations of Browne:
https://babel.hathitrust.org/cgi/pt?id=mdp.39015001517492&view=1up&seq=41&skin=2021&q1=%22anthony%20browne%22
An article in Notes & Queries from 1887 quotes the 1540/1 will of Francis Browne, father of Joan (Browne) Hone.
https://www.google.com/books/edition/Notes_and_Queries/t7URAAAAYAAJ?hl=en&gbpv=1&dq=%22francis+browne%22+beatrix&pg=PA464&printsec=frontcover
This article mentions Francis' first wife Margaret Mathew, as well as a second wife, "Beatrys my Dame," named in the will. Beatrice was living as late as 36 Henry VII.
_Early Chancery Proceedings_, vol. III (? 1963), in the "Lists & Indexes" series reveals the probable birth identity of Beatrice:
[File 947, no. 51]
Francis BROWNE, esquire, and Beatrice, his wife, daughter of George Makworthe and late the wife of John, son of John Rowley, citizen and ironmonger of London v. Edward DUDLEY, and Jane his wife, executrix and late the wife of the said John [Rowley], the elder [concerning lands, goods, and money promised to Beatrice upon her first marriage].
https://www.google.com/books/edition/Lists_and_Indexes/sewMAQAAIAAJ?hl=en&gbpv=1&dq=%22edward+dudley%22+%22john+rowley%22&pg=PA18&printsec=frontcover
Mackworth is another gentry family in co. Rutland.
It seems likely that the Joan Browne married Hone was a child of the first wife (Margaret Matthew), but there may have been children of Francis Browne by Beatrice (Mackworth) Rowley, as the N & Q article mentions that the son William may have been born 1539. Supposing Joan was married early (at say age 15), there is a slight chance she might be by Beatrice, not by Margaret. The chronology of the Rowleys of Rotherhithe should be checked.
Hatcher mentions that William Hone was seized at death (1575) of an inn and four adjoining shops in St. Botolphs without Aldergate. She also gives his father as John Hone, citizen of London (based on the Essex Vis. pedigree).
An Inquisition post Mortem taken in August 1538 for a John Hone, tallowchandler of London, mentions a messuage or tenement and four shops adjoining in "the parish of St. Botolph without Aldrichegate."
https://www.google.com/books/edition/Abstracts_of_Inquisitiones_Post_Mortem_R/amtKAAAAYAAJ?hl=en&gbpv=1&dq=%22william+hone%22+brown&pg=PA51&printsec=frontcover
This very likely gives more information on the father of William Hone (who married Joan Browne), including that his father John Hone left a will and had a widow Cecilia, who remarried before the date of the Inquisition to one John Baynton.