Other thread, looking for info on Home Children. Sadly unless confirmed by other sources, the parent's first names may not necessarily be correct. Have you a source for the names Wm. & Mary?
https://www.rootschat.com/forum/index.php?topic=885554.0The Fitzjohn/Pond marriage took place at St Leonard's, Shoreditch which is an Anglican church. This doesn't necessarily rule them out entirely, as perhaps only one spouse was Catholic.
https://www.familysearch.org/ark:/61903/1:1:84KX-ZNZMA Frederick, with mother Pond ( the only result for Pond maiden name, sadly)
GRO Reference: 1862 D Quarter in DOWNHAM UNION Volume 04B Page 371
FreeBMD has an Annie Louisa Fitzjohn - Birth registered March Quarter 1861
Whitechapel Whitechapel Vol. 1c p.410 but sadly no results on GRO!
https://www.freebmd.org.uk/There's also a death registered for a Mary Fitzjohn age 40 Whitechapel Vol. 1c p.305
If this turns out to be your Mary the father may have put the children into care.
Oddly...Had I not seen the Pond marriage online, I'd have looked into the Caton surname - on the same result as Pond...as there is only one GRO result for a James (thought to be brother of Wm/John)
1865 June Quarter WHITECHAPEL Vol. 01C p.386
But surname Caton doesn't seem to come up with a Fitzjohn marriage except that match disproven above?
I see that someone else has claimed a different couple to be your ancestors...even though the dates, & other info don't match up...
https://www.familysearch.org/tree/person/details/LH1W-CHT