Estwick was born about 1657, or earlier, if it be true that he was one of the first set of children of the Chapel Royal under Cooke, after the Restoration, and a chorister at St. Paul's Cathedral at the same early date.
Estwick was probably too sympathetic and constant a frequenter of the rehearsals of music held weekly in the Dean's lodgings, to fall under the extreme penalty dealt unto delinquents by the genial host, namely; the restriction for the one evening to small beer, and exclusion from the next meeting.
He was not only an excellent and zealous performer in the choral duty until extreme old age rendered him incapable of it, but a remarkable fine reader also.’ He became sixth Minor Prebend at St. Paul's Cathedral in 1692; senior cardinal, or Superintendent of the Choir, in November 1698, and Sacrist on the death of James Clifford in February 1698-9.
Estwick was appointed vicar of St. Helen's, Bishopsgate, in 1701, and rector of St. Michael's, Queenhithe, in 1712, but he continued to perform his choral duty at the cathedral till near the time of his decease, ‘when little short of ninety years of age.
Bending beneath the weight of years,’ Hawkins goes on to say, ‘but preserving his faculties, and even his voice, which was a deep bass, till the last, he constantly attended his duty at St. Paul's, habited in a surplice, and with his bald head covered with a black satin coif, with grey hair round the edge of it, exhibited a figure the most awful that can well be conceived.’ He died on 16 February 1738-9.