Without purchasing all the certificates it is not possible to confirm which of the linked children were those of John Joseph and Edith BROWN. I have listed the most likely, but there were at least three other BROWN men who married SCOTT women whose families these children may belong.
Eileen is the most likely as she appears in the 1939 Register with Edith's mother, albeit as Eileen B SCOTT.
There was another BROWN child born with maiden name SCOTT: Barbara B BROWN in 1921, however she appears in the 1939 census with another BROWN/SCOTT family.
An Edith BROWN, aged 28, died in Q4 1923 in West Derby. This might explain why Eileen was living with her grandmother. The later children may have been other families' children.
An Edith BROWN, born c.1895 died in Liverpool in Q3 1941, aged 46. Liverpool suffered more civilian deaths in the blitz than any other UK city outside London.