Harry was reported by JJ Brough to FW Brough (both of whom knew him) in his 1947 letters to have been Ruth Symmonds illegitimate son, probably following an affair that Ruth had with an Italian waiter. This is consistent with his presence with his grandparents in Lewes in the 1871 census. So this seems to be certain. He was her illegitimate son.
On the face it, Harry was thus born in late 1862 or early 1863, in Eastbourne, where Ruth had been with her parents in the 1861 census. She may by then have been in service in Brighton. Certainly, there is a birth of a Henry Simmonds registered in Brighton in 1862. So she might have conceived the child in either Eastbourne of Brighton, and given birth at her parents house (common practice in those days), and then registered the birth in Brighton. We do not have the birth certificate to hand as yet to confirm this.
All the above seems plausible. Indeed, quite normal for mid 19th century illegitimate births. Except that Ruth was quite clearly only born in 1848, so she was only 22 or 23 by the time of the 1871 census — yet Harry was reported by his grandparents to be 8 at that time. Which would make Ruth only 14 or 15 when she gave birth! Possible, but very, very unusual. [Note that girls/women could marry once they were 12 until the 1920s in England. But births at such a young age were quite exceptional, and the mean age at which girls would have been able to conceive in 19th century England was probably about 16 (as opposed to the 12 to 13 of 2000).]
Given this discussion, the birth of Harry in 1862/3 must be considered putative as yet, until a birth certificate can be obtained.