Hello Pat & Debbie,
I posted the 1916 Census to see what Pat thought because she is working on very little information but it seems there are many cooincidences with this family. You are correct no other children have been mentioned yet.
I agree with all that Debbie has written re: the marriage and birth of Alice Elizabeth, the occupation of Harry changing from carman to painter seemed insignicant.
If you look at the London births for Harry - perhaps he was'nt a McKay. The London births give Harry Richardson born 26 Aug 1899 and baptised 27 Sept 1899 to Harry Richardson (soldier) and Sarah Richardson. The address is 23 Gilroy Square.
On the marriage of Harry McKay to Sarah Richardson 21 July 1902 the address is 23 Gilroy Square.
They had moved to 22 Millman Street by the time Alice Elizabeth was baptised in March 1903
London Baptism:-
Name: Harry Richardson
Date: 27 Sep 1899
Father's Name: Harry Richardson - Mother's Name: Sarah Richardson
In The Parish: St Luke, Chelsea and the Borough: Kensington and Chelsea. Middlesex
Sarah’s father George was deceased when she married Harry, it looks as if he could have died 1888 Chelsea. What seems peculiar is that on the 1901 census for 23 Gilroy Square, Sarah Richardson is with her mother Sophia who seemingly has remarried to Robert Richardson (an entry March 1895 Chelsea 1 a 486 but the marriage entry does not show Robert Richardson) and the census does not show Harry born in 1899

1901 23 Gilroy Square. Chelsea.
Robert Richardson 45
Sophia Richardson 43
Sarah Richardson 22
George Richardson 18
Alice Richardson 14
Edward Richardson 10
Charles King 7 AMENDED TO SHOW CHARLES KING
T Cross 43
C Cross 34
George Cross 13
Willie Cross 9
Alice Cross 6
Rose Cross 4
Lily Cross 2
Emily Cross 5 months
So I still strongly believe that this is the correct family and would'nt want to discount them yet.
Regards
Sandra