Henry Carrington was a major influence on the Bowles Family of Printers/Publishers in London in the 1700's.  The most obvious impact would be the lending of his surname Carrington as a given name to many generations of Bowles to follow.  The London printer and publisher John Bowles (his father was Thomas Bowles I who had established the family business)  had married Henry's only child and heir, Mary Carrington, in 1722 and a son Carington Bowles was born in 1724 and a daughter Mary Bowles either just before or just after the boy.  Her birth record has not yet been identified for certain.  In any case Mary Carrington Bowles died in 1730.  The timing might indicate that she died in childbirth but no baptismal record for such a child has yet been found. 

See the case for there having been one additional child in the Carrington/Bowles line of descent.  See The Thomas Carrington Bowles of Maryland Mystery

Will of Henry Carrington, dated Sept. 16, 1757, proven at London March 8, 1757

Henry Carrington of Charles Square, St Leonard Shoreditch, Middlesex, Gentleman being in healthy body (etc. as usual)

Whereas in and by an indenture quadripartite bearing date on or about the 18th day of October in 1743 made between Richard Froome of the first part, John Bowles and his daughter Mary Bowles spinster of the second part, me Henry Carrington grandfather of Mary Bowles of the third part, Joseph Watson since deceased and Valentine Lawford of the fourth part (purporting to be a settlement made previous to the marriage of Mary Bowles with Richard Froome)  I Henry Carrington did grant to John Bowles Joseph Watson and Valentine Lawford that my executors should within one month after my decease assign unto John Bowles Joseph Watson and Valentine Lawford in the books of the Bank of England 3,350 pounds 3% annuities for the year 1743 and all interest dividends and profits thereof to and for the uses therein declared of and concerning the same I do hereby (as far as in me lies) ratify and confirm the said deed and do instruct my executors within one month after my decease to transfer unto John Bowles and Valentine Lawford the surviving trustees named in the said deed the 3,350 pounds as above and whereas in and by one other indenture quadripartite bearing date March 26, 1752 made between I Henry Carrington of the first part my grandson Carrington Bowles of the second part Ann Field spinster the youngest daughter of Joseph Field of the third part, the same Joseph Field Joseph Field the Younger John Bowles father of Carrington Bowles and Thomas Bowles (note: this would be Thomas II in the family tree) of the fourth part purporting to be a marriage settlement previous to the marriage of the said Carrington Bowles and Ann Field, I Henry Carrington did covenant and agree with Joseph Field the Elder Joseph Field the Younger John Bowles and Thomas Bowles that in case the said marriage did take effect that my Executors should within one month of my decease transfer to the above four the sum of 4000 pounds shared interest in the Joint Stock of 3% Bank Annuities (and so instructs his executors)

Also I give to John Bowles one of the trustees of the said marriage settlement (so John I)  50 pounds share in the joint stock of 3% annuities for the year 1726 within one month etc. Also I give to John Bowles, Carrington Bowles and Richard Froome 900 pounds share in (the same) for the year 1726 etc. (as above) and of that 900 pounds his executors to transfer 225 pounds from time to time until my great grandson John Froome son of Richard Froome and Mary his wife shall attain the age of 21 and a further 225 pounds (of the same) to Henry Froome and a further 225 pounds until my great grandson Carrington Froome shall attain 21 and the last 225 pounds until my great grandson George Froome shall attain 21 and if any of them shall die before the age 21 their share to be equally divided amongst the others All the residue of my estate after the discharge of my debts and funeral expenses to my grandson Carrington Bowles who I also do appoint to be my executor

To this I do set my hand and seal Sept. 16, 1756 Henry Carrington
Witnesses: Mary Esridges (or Etridges) Jane Miller Thomas Hunt  

Will proven at London March 8, 1757 by the oath of Carington Bowles grandson of the deceased and sole executor

Images of the probate office copy of his Will: