RootsChat.Com

OK Forget the City and Counties Directory entry. It is dated 1864 when Samuel was 11 and it is a Confectioner.

Probably same family though.

The problem with census returns is the fact that not 100% of the population are recorded.

OK If you are the Smith family living at  2 Jones Street Anytown you are virtually going to be recorded.

What the census form says is record people who were in your household on the night of 31st March, the couple didn't have a fixed address and although the landlady stated they had lived with her it's possible they spent the night somewhere else, or it's possible she was only allowed to have one lodger who she did declare.

My way forward would be to get a copy of the unknown female death certificate to see what the cause of death was, if it was found drowned in the Thames then see if you can find more detailed information about the unknown female burial from the cemetery records, if it says found drowned in the Thames I think you will have found her. She will have been buried in a common grave.

What about this death

Female
Age   24
Estimated Birth Year   abt 1877
Registration Quarter   Apr-May-Jun
Death Registration Place   Woolwich, London, United Kingdom
Death Date   Jun 1901
Inferred Death Place   London, United Kingdom
Volume   1d
Page   658

https://digupyourancestors.com/2020/04/04/a-person-unknown-drowned-in-the-thames/

This makes interesting reading. I found it whilst looking for a couple of my ancestors who committed "suicide" in the Thames.

Interesting but that covered the 17 hundreds we are talking about the 1890s here.

As far as I can see the OP has absolutely no evidence of anything connected with their story.

Saying there must be something in the family story is not always true.

 My family story is our connection to the Jennings millions (( google it ) . 

Doing my family research I found the man who brought the Jennings name into the family wasn't born with that surname, he was illegitimate and his mother later married a Mr Jennings whose surname he took. I have no DNA I can trace to Mr Jennings so the line is extremely tenuous to say the least.

The problem back in the 1890s is that people didn't walk round with a pocket full of ID documents like they do today. No Drivers Licence, no bank card easily no passport, people travelled the world without passports.

OK A local found drowned could be identified, someone would come forward  with a description and they would identify the body.

Two people from thousands of miles away, no ID they would not be identified and no one to notify family.

I think if it had happened and family had been informed there would be something in local NZ newspapers.

I think someone somewhere drowned in N Z and a story became garbled. Could be something like ' that river is as big as the River Thames in London'

What happened to Polly?  My guess she left for some reason and reinvented herself somewhere else.

Maybe DNA results could throw up an unknown line who were descended from her.