If we're thinking his parents are Alfred William Millard and Margaret Elizabeth Screech then this appears to be the family:
GRO BMD references:
1885 Q3 Marriage: Alfred William Millard & Margaret Elizabeth Screech; Kingston; vol 2a; 515
1939 Q2 Death: Margaret Elizabeth Millard; age 78 (born c1861); Camberwell; vol 1d; page 594
1940 Q1 Death: Alfred William Millard; age 76 (born c1864); Greenwich; vol 1d; page 1615
1886 Q3 Birth: Horace Alfred Millard (mmn: Screech); Guildford; vol 2a; page 60
1888 Q4 Birth: Stanley Wheeler Millard (mmn: Screech); Lambeth; vol 1d; page 522
1890 Q3 Birth: Leonora Helen Millard (mmn: Screech); Lambeth; vol 1d; page 470
1893 Q2 Birth: Ethel Florence Millard (mmn: Screech); Lambeth; vol 1d; page 493
1899 Q1 Birth: Reginald John Millard (mmn: Screech); Lambeth; vol 1d; page 539
1901 Q3 Birth: Henry William Victor Millard (mmn: Screech); Lambeth; vol 1d; page 505
1913 Q3 Marriage: Vere V T Dishart & Ethel F Millard; Camberwell; vol 1d; page 1785
Probate
Alfred William Millard
of 27 Tudor road Woodside Surrey
died 8 Jan 1940
at St Alfeges Hospital 48 Vanbrugh Hill London
Admin
to Horace Alfred Millard, ambulance driver
and Reginald John Millard, sergeant, HM Army
https://probatesearch.service.gov.uk/Calendar?surname=millard&yearOfDeath=1940#calendar1911 Census - Lambeth
Alfred William Millard & wife Margaret
https://www.familysearch.org/ark:/61903/1:1:XW57-WF3Also, Horace can be located in 1939 but it may depend on what source (Anc or F M P) you're using.
EDIT: Corrected name of Horace named on probate record of possible father. Horace William Millard => Horace Alfred Millard. (Thankyou, LM).