Thanks for looking into that, Henry- I think you're quite right, there's no link as far as I can see (unless perhaps one looked back through records etc)! I had a bit of a dig re: Barming House, which seems to be at Maidstone, Kent, and there doesn't seem to be any obvious connection there either, the notable figure in that family seeming to be Capt. Charles Whitehead (1834-1912), late West Kent Queen's Own Yeomanry, F.L.S., F.S.A., F.R.G.S., F.G.S., J.P. and D.L., who m. Catherine Laetitia, dau. of Richard Elliston Phillips Balston, of Thornhills, Maidstone, and had issue [some details here-
http://tonbridgeatwar.daisy.websds.net/Authenticated/ViewDets.aspx?RecID=405&TableName=ta_factfile ]
Of course, the details in the tree on the Bolton School site are rather limited with regard to the earlier generations, so it's not impossible there's some more distant connection I suppose!
EDIT: my eye caught "Sir" in another source as I was typing, which on closer examination doesn't seem to apply to Charles Whitehead; additionally, Walford's County Families 1886 gives Charles as "son of the late John Whitehead, Esq., of Barnjet, Kent (who d. 1879) by his 2nd wife Mary, who d. 1884, eldest dau. of the late Thomas Milles, Esq.". "Barnjet" allowed for a search in BLG 1898 (from which came the above details of Charles Whitehead), giving the following lineage down to John Whitehead (as above), which, being I recognise only tangentially related to the topic of this thread, I include more for completeness's sake than relevance:
"The Rev. Charles Whitehead, M.A., formerly Fellow of Clare Hall, Cambridge, Vicar of East Grinstead, m. 1754, and d. 1792, leaving issue:
1. Charles, of whom presently.
2. Gervase (Rev.), B.D., Fellow of Jesus Coll., Camb., Vicar of All Saints, Cambridge, and of Seal, Kent, Chaplain to the Duke of Dorset, b. 1763, d. 1838.
The elder son,
Charles Whitehead, of Ash Place, Kent; m. 1791, Mary Miller, and d. 1833, leaving by her (who d. 1820) a son,
John Whitehead, of Barnjet, Maidstone; m. 1833, Mary, dau. of Thomas Milles, of Buston, Kent"