Aaron Rayner

Of children born in time period after their marriage, three possible children were found in Free BMD search. From FreeBMD Births Mar 1916 :-

Surname: Rayner First name(s): Sidney S Mother: Marks District: Mile End Vol: 1c Page: 651

Surname: Rayner First name(s): Sadie S Mother: M[ae]rks District: Mile End Vol: 1c Page: 651

From FreeBMD, Births Sep 1926 :- Surname: RAYNER First name(s): Milton M Mother: Marks District: Stepney Vol: 1c Page: 288

Possibly the middle initial "S" in Sydney's name is Solomon - named Shlomo after his grandfather. Grandfather Solomon was still alive (d 1917), but unlike Eastern European Ashkenazim who do not name after the living, Dutch Ashkenazim may do.