MWS, thanks for the further info. including the Harriet Swinson link and the name of Dorothy Holland. As you say, the link to Swinson may be through Jane's mother.
Howard Leathlean (Thesis; University of Reading, 1989: H.N.H. The Work of Henry Noel Humphreys) agrees with 1807 as his birth (my date came from Ray Desmond's "Dictionary of British & Irish Botanists, which is usually pretty reliable; that date is also quoted in the DNB). As MWS mentions, there were a range of dates given in various obituaries, etc, but the one given in "The Garden", which is likely to be accurate since William Robinson (the writer and proprietor) knew HNH, is 1807. Leathlean includes some family details, gleaned from a memoir dictated by HNH's son, Noel Algernon Humphreys and also a journal kept by the same. Quotes below are from Leathlean's Thesis.
HNH's grandfather was George Humphreys, who "lived at Sparkbrook and was a member of the Lunar Society".
I have since discovered, from contemporary newspaper reports, that George Humphreys was a "Protestant Dissenter", and nominated to be on the committee of the district of Warwickshire (along with Wm. Russel, Joseph Priestley, John Ryland, William Hutton and others). (Derby Mercury, 21 January 1790, page 3). In the "Priestley Riots" of 1791, George Humphreys' house was ransacked, but not burned down. (Various newspapers, late July 1791). He was partially compensated for the damage in 1792. (Norfolk Chronicle, 14 April 1792, page 2).
George Humphreys' son (HNH's father) was James Humphreys, who "had the reputation of being a spendthrift and unwary investor. He is believed to have become involved in an expensive lawsuit in Belgium. He was there at the time of the Battle of Waterloo ... James Humphreys' profligacy or recklessness most likely prompted his wife, Dorothea Ann Knowles, to found the Ravenhurst School for Girls at Sparkbrook so as to supplement the family income. She was the daughter of Guy Knowles, a Birmingham doctor, and the sister of George Beauchamp Knowles..."
Leathlean also mentions a pamphlet "Humphreys on Manures" published by Longmans c.1844 by "J. D, Humphreys" (this based on info gleaned from the Longman archives). "On 6 June 1859 the remaining 137 copies [of an edition of 250] were written off. Superadded to J.D. Humphreys's name is a concise statement of finality: "dead"." Leathlean gives additional details as to why this J. D. Humphreys is likely to be HNH's father. I have not traced any copies of the pamphlet (yet) nor have I discovered anything in newspapers relating to Humphreys- nor the pamphlet! Ravenhurst School for Girls is also elusive.
Another snippet of information about HNH's family is "This print may be one of the series to which young Noel [i.e. Noel Algernon] referred to in his journal on 30 May 1852: "In the afternoon Aunt Harriet showed me some drawings that Papa had made when he was a little boy..."." So there is a Harriet in the family, presumably sister of Henry Noel Humphreys or of his wife, Dorothea Ann.