Resourced from R.O. Bucholz The Data Base of Court Officers: 1660 - 1837 was the name of a footman named William Peach.
Peach, William Footman to Anne, Princess of Denmark occ. Est. of [?1685]-July 1689 (Add. MS. 15897, f. 55; LS 13/231, p. 49). No further occ. Footman 6 July 1702 (LS 13/199, f. 10; LS 13/200 f. 18v). D. by 19 Sept. 1721 (LS 13/200, f. 57).
and my confirmed ancestor, below, where the Royal Household records also has his name as Peach:
Petch, William Page of the Backstairs 31 Mar. 1770 (LS 13/203, p. 82; see Papendiek Memoirs, p, 323 n. 59, for ev of app. Apr. 1767, having previously been a page to Edward, Duke of York). D. by 11 Apr. 1771 (Ibid., p. 92).
Peach (Patch), William Page of the Backstairs to Prince Edward, Duke of York occ. 1762-1767 (CCR [1762], p. 100; last occ. ibid. [1767], p. 94). Vac. 17 Sept. 1767 on d. of Edward, Duke of York.
I have accessed Charlotte Papendik's Journal and she confirms with numerous incidents that William Petch was the King George 111's Page of the Backstairs (hairdresser), as her father Frederick Albert was Queen Sophie's German born hairdresser.
If the footman William Peach died before 19 Sep 1721, then he still could be grandfather. rather than father as my ancestor was born c1730 based burial in 1771. [Folklore Lady Petch only daughter of an Earl]
My request for help is asking for others who may have better access than I, to find more about the William Peach who died before 19 Sep 1721, assumed in London; a possible wife; and children.
Keith