Given that Harry married in Macclesfield district in 1925 and appears to have remained there for several years, I would investigate the following very closely:
1. The births of two children who died young, May (1921) and George (1924) Simmonds, whose mother's maiden name is listed as Oldfield. There is another child later on with "Simmons" as a surname.
The parents may be George "Simmins" and Carrie Oldfield who married in Macclesfield in 1919.
https://familysearch.org/ark:/61903/1:1:FQP4-NLY - this gives George as 58 years old, e.g. born around 1861, and his father was Thomas.
His bride appears to have been born in 1890 (she is still on the 1939 index), and was from the Macclesfield area (her father is Benjamin and her family are easier to trace).
2. The death of George Simmonds in Macclesfield in 1934, aged 75. This would put him as born about 1859. This is probably the same man who married Carrie Oldfield.
So this gives us a possible for Harry's father, as George born 1859-1861ish, and in Macclesfield by 1919, but it doesn't make it any easier to trace them in earlier censuses!