Need help finding Thomas Turner, Engineer with daughter Elizabeth Rebecca Turner born circa 1842 London

Question

I've hit a bit of a brick wall with my 3rd great grand father & mother.  The only details I know are from his daughter Elizabeth Rebecca Turners marriage to William Raddon Arkley: Thomas Turner, engineer.  Citation: London Metropolitan Archives; London, England; London Church of England Parish Registers; Reference Number: P72/BAT/017

I have searched many census records, even resorting to searching just Thomas, Elizabeth & engineer, in case incorrectly transcribed.  I have only found 2 census records, both of which I now think are incorrect.  These are as follows:

NOT Thomas Turner, BIRTH 1820 Gravesend, living at 17 Grosvenor Street, Stepney in 1851, then 8? Limehouse in 1861 because in 1881 Elizabeth is living with them as Elizabeth Harris, married with children

NOT(?) Thomas William Turner, BIRTH 1813, Dockhead, Surrey, England, living at 46 Surrey Row, Southwark Christ Church, Surrey, England, Widow, living with Thomas Surner 31 Charles Surner 10 Henry Surner 8 Elizabeth Surner 4 Dinah Liscomb 55 (servant) Elizabeth Liscomb 24 (visitor).  This one is still on Elizabeths profile as I think I've only disproved it this morning.  Found another researcher on ancestry who had this Elizabeth Turner marrying a George Morgan and marriage record (citation: London Metropolitan Archives; London, England; London Church of England Parish Registers; Reference Number: P92/PAU2/011) states father as Thomas William Turner and further census records for Elizabeth Morgan match birth year and place, whereas my Elizabeth Turners birth year and place don't match exactly.

I have not been able to find christening records for Elizabeth to help either.

Any help you can give would be greatly appreciated as this is the only set of 3rd great grand parents that I am missing.

Comments

It doesn't help that in more than one census her place of birth has changed from Middlesex to Cambridge, Cambridgeshire.
(One of the sons did some fancy stuff with his name.  Sure beats my grand-aunt!)

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You're right it doesn't help.  I'm pretty sure this is still the same person though even with birth year and place changing because the children that are living with her still match.  The other 3 census records before that all match so I would presume somehow a mistake was made on that census?

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I wouldn't presume a mistake.  people reinvented themselves for various reasons.  They didn't have the same fixation on names being the same all the time. (Berty becoming Bertie, then Albert, then Herbert Anthony.  (Where did that Anthony come from?  Is he even the same person?))
Dates were more fluid, too, as people would either get younger in a ten-year period, or would drastically age!  (And males did it every bit as much as females.)  Birthdates being something absolutely fixed in stone seems to be a 20th century thing -- and not even then if you go by what some people claim (I tell my grandkids I'm never getting older than 18).