Hi, Pete's friend here. This is the info that Medway Archives sent me, which is where we got Eliza Collins from:
"The creed register (ref: WIc/, microfilm 167) shows that Reginald Elliott was admitted from Strood Intra on 11 August 1902, and discharged on 27 July 1904. The name of the informant is given as Mrs Elliott. The same page of the creed register shows the admission of two other Elliotts, Bertie and Minnie, who were admitted on 6 March 1902 from Strood Intra and also discharged on 27 July 1904. . The name of the informant is given as 'aunt'. The name of the pauper's nearest relative or friend is given as 'Eliza Collins, 5 Pearson Street, Station Road, Strood.'
The admission and discharge register for 1902 (ref: WIa/2, microfilm 161) confirms this information. P. 41 shows the admission of Bertie and Minnie Elliott. Bertie was aged 9 and born in 1893, and Minnie aged 6 and born in 1896. They were brought in by their aunt Eliza Collins of the address mentioned above. P. 65 records the admission of Reginald Elliottt, aged 4 who was born on 1898. No extra notes accompany his admission."
I feel that it would be worth getting the birth certificate for Reginald Banks (and/or Herbert or Minnie) as it would establish whether the mother was Eliza, who Frederick appeared to be married to, although I haven't yet found a marriage cert, or Minnie, as stated on the baptism.