In the brief memoir of Beddome published with the sermon collection of 1835 we read of Beddome's conversion. The writer says young Beddome's mind
appears to have been altogether unimpressed about religion, till an event occurred which he himself thus records. "Mr. Ware, of Chesham, uncle, I believe, to Coulson Scottow, Esq. preached at the Pithay, Bristol, August 7, 1737, with which sermon I was, for the first time, deeply impressed. Text, Luke xv. 7: 'Likewise joy shall be in heaven over one sinner that repenteth, more than over ninety and nine just persons that need no repentance.'" Thus more than twenty years had been devoted to the service of Satan, notwithstanding the numerous and affectionate discourses of the pulpit, the prayers, instructions, and examples of his parents; but when he heard the character of the penitent described, it at once became his own. Indeed, so intense were his feelings, that as he could not suppress his tears, he selected the most retired part of the chapel to conceal them; but though his grief was thus hid from man, it was doubtless the cause of joy among the angels in heaven ....
I have wondered about the identity of this Mr Ware and finally more or less tracked him down. He was Joshua Ware (d 1739) and he was indeed uncle to Coulson Skottowe (1719-1784). He was a gentleman perhaps a knight and, it seems, a medical doctor.
An article about the Skottowe family (the K is now preferred) here quotes from a privately printed book from 1963 by Philip E Skottowe called The Leaf and the Tree that says
A Mr [John] Ware, who was the High Sheriff [of Buckingham in 1735], had three beautiful daughters; his brother [Joshua], who was minister of the Baptist Chapel in Chesham, paid a visit to a friend named Coulson in Yorkshire, probably John Coulson [d 1674], the uncle of Elizabeth [Coulson], wife of Thomas Skottowe (1695-1771). The reverend gentleman spoke so highly of his nieces' charms that Coulson asked to see their portraits and finally selected one [Martha] as his wife. Her sister Rebecca, while on a visit to her newly-married sister, met young Thomas Skottowe and became his first wife in 1717, dying after the birth of her son Coulson in 1719 [his second wife was Anne Casrip d 1751].
So one sister, Martha, married the elderly and wealthy Presbyterian merchant, John Coulson, while the other sister, Rebecca, married 21 year old Thomas Skottowe from Norfolk (a twin whose brother Coulson died 1750; the patron of sea captain James Cook who so inspired William Carey). A point of interest with regard to Skottowe's marriage is that it was, as a lawyer later described it, 'a stolen match', without the permission or approval of the well-connected Ware family of Chesham. This fact had important consequences. It meant that the impecunious Skottowe did not receive the marriage portion customary for those of his class. It also meant a breach between him and his powerful in-laws which was shortly to lead to a major humiliation.
It is clear from John Coulson's 1727 will that he and the Wares strongly disapproved of Skottowe. The will was apparently a ruthless document in which Coulson used his financial clout to humiliate Skottowe in his role as a father. It demanded that Skottowe hand over his son, Coulson Skottowe, then aged eight, to the guardianship of the Ware family, the family of his deceased mother, Rebecca. Three guardians were nominated, who would henceforth be entirely responsible for his upbringing and education. These were his aunt Martha, her father, John Ware, and Coulson's uncle Joshua, the man through whom Beddome was converted. From then on, Skottowe could have nothing to do with his son and was forbidden to attempt to get him back under his own control. He was to sign legal contracts agreeing to all this. If the terms were met, he would receive £500 under the will. When Coulson Skottowe came of age he would inherit all John Ware's property. If the terms were broken he would inherit nothing. At the time of John Coulson's death, his father-in-law, John Ware, was living in a house in South Shields, so presumably the boy then went to live there with his aunt and his great uncle. Hence Beddome's "uncle, I believe, to Coulson Scottow, Esq".