https://www.freebmd.org.uk/ has three Baggaley births, mother maiden name Smith:
Geoffrey Ecclesall Bierlow 1929
Dorothy Sheffield 1931
Joan Sheffield 1938.
Possibly members of your target family.
Doris is on the 1939 register. With her is son Geoffrey b 1929 and there are no redacted entries. There is another Baggaley Smith marriage in the area in the 1930s so presumably the other 2 belong to them.
Dave
https://probatesearch.service.gov.uk/ has some information about the 1949 probate file of John Wilfred Baggaley of 4 Khartoum Road. Widow's name is Doris Sylvia.