Great post, Troy. I knew nothing about Adkin, and had to scramble a bit to dig up some information. It's clear that they were a tiny addition to the formation of the Imperial trust, receiving about 1.2% of the equity and perhaps half that percentage of the advertising budget in the early years. While not the smallest company invited to join, my guess is that they (along with other minor tobacco manufacturers) were asked at least in part to present the image of a more united industry front against Duke's assault: a sort of "coalition of the willing" formed to beat back the American invader from British soil.
As for the company itself, it's easy enough to find a few websites that assert it was established in the late 1700s. After some quick research, though, I'm skeptical, and more inclined to believe it dates from the 1820s or more likely 1830s. Certainly the earlier London directories don't list an Adkin in the tobacco trade. More importantly, tracing the genealogical line back from the time of the Imperial merger we learn that the founding family consisted of Robert Adkin and his wife Margaret Ann Whitley; I would guess both were born around 1790, plus or minus five years; certainly they were married in March of 1814, and had four children before Robert died: three sons named Robert Whitley Adkin (1816-1884), John Adkin (~1818-1907), and Charles Adkin (1820-1891), and a daughter named Catherine (1821-1859).
Robert's trade is uncertain. Other than the marriage record, which doesn't state an occupation, the only references I've found refer to him variously as a "gentlemen" (these occur decades after his death, and of course are uninformative), a silversmith, and a jeweler. Nowhere does it say tobacco manufacturer. My guess, and it's only that, is that either he entered the tobacco business very late in his life, or his widow Margaret entered it after he died. It's clear that Robert was dead by 1839, since a London directory survives from that year listing a tobacco manufacturing business called Margaret Adkin & Son. Presumably the "son" in question is Robert Whitley, since he was the eldest of the three boys. At that time the business was located on Ratcliff Highway; Adkin's specific section of the highway was called St George's Street East, and both names are used in various directories and Gazette notices. Adkin remained there at least through 1852, although by 1863 it had moved to 31 Aldgate. Note that sometime around 1842-1843 the name is changed to Adkin & Sons, implying the entry into the business of one or both of the other brothers (all three were eventually involved). In 1850 their sister Catherine married a man named William Charles Bartholomew Hockly (1822-1890), and he also shows up as a partner in Adkin & Sons, as eventually does his son by Catherine, William Wellesley Hockly (1854-1902).
It is the next generation that apparently engineered Adkin's entry into the Imperial trust, and compensated for a loss of independence with a rather large pile of cash. Robert Whitley Adkin had three children; the oldest, a boy named Henry John (1858-1921) became a solicitor, and was not a partner in the tobacco business. The middle was a daughter named Edith Marian (1859-1886), and died unmarried. The youngest was a boy named Francis Newbery (1861-1947), and he was the one to take up his father's role in the tobacco business. Note that while father Robert Whitley was worth 41k pounds when he died in 1884, his son Francis Newbery was worth 123k pounds upon his death in 1947. Pretty impressive considering the confiscatory taxes put in place in the UK during and after the two world wars.
Robert Whitley's younger brother, John Adkin, had six children, four boys and two girls. Of this brood, two played the more important roles in the tobacco business: oldest child Robert (1849-1935), who left an estate of an astounding 295k pounds, and next oldest son John Gibb (1852-1923) who left an almost equally impressive estate of some 153k pounds. Their father John, who died in 1907, by comparison had left an estate of some 51k.
The last of Robert and Margaret's sons, Charles Adkin, had only one child, a daughter named Hannah Mary Adkin (1854-1950). She married a man named Charles William Startin, and from what I can tell they were uninvolved in the family business.
And as noted, daughter Catherine's husband WCB Hockly and their son WW Hockly were each also partners for a time, but in WCB's case he retired from the partnership in 1885 and died five years later, while the son WW retired in 1890 and died in 1902. So neither member of this branch were still partners at the time of the Imperial merger, and able to profit form it. Their estates were correspondingly lower at the time of their deaths.
So of the Adkin family, when the Imperial deal came along the surviving members still involved included one of Robert and Margaret's sons, John Adkin, along with three of their grandchildren: two by John Adkin (Robert and John Gibb), and one by Robert Whitley (Francis Newbery).