You have few opportunities to see good recorded information about the people you are researching, in England, because BDM records for that time give little information.
Having moved to Victoria, in which location BDM certificates record good information, you are well placed to find useful clues to the origins of your ancestors.
Sarah died first, with husband as informant, so you would expect this information to be credible. Husband John has known Sarah longer than has anyone else around when Sarah dies.
John MITCHELL died several years later. The agent is the notional informant, the medium for registering information given by......who?
Possibly an adult son/daughter.
You need to give close, questioning attention to BDM documentation. You should include date and place of the death registration. If eg. their is a gap of many days you might wonder why....might mean something, might mean nothing.
Why, for both certificates, is son Robert recorded as deceased?
Work down a generation. What names do you see for children of these MITCHELL sons and daughters.....grandchildren of the MITCHELL-ANDERSON couple?
Often clues (as names) can skip a generation. The children of John MITCHELL and Ann ANDERSON might use family names from their MITCHELL/ANDERSON ancestry for their own children.
St Kilda Cemetery
https://smct.org.au/deceased-search MITCHELL Sarah
Baptist, Compartment B, Grave 060 date of Service 22 Apr 1889
MITCHELL John
Baptist, Compartment B, Grave 060 date of Service 9 Sep 1895
There are usually four burials in a plot. You could contact the Cemetery, give the plot reference, and ask who else is buried in the plot. Might be a surprise find.
And the certificate for John MITTCHELL's second marriage in Victoria would have information that John gives about this origins...first hand information.
Read through other posts on Rootschat and see how all details from source records have been used to advanced family history research.
