According to her marriage he name is Florence Olivia Ringer and it gives her fathers name as James.
Two questions:
Does the marriage certificate give an occupation for James?
Who were the witnesses?
Given that Plaistow is in the West Ham registration district I thought I would have a look for any RINGER and any Olivia there. Accidentally, I clicked 'all types' instead of 'births' and saw:
Marriage Dec qtr 1873 West Ham vol 4a p51 - Olivia RINGER - same page as Keziah TANDY, Arthur SMITH and James WOLNER). A quick search of the GRO birth index showed baptisms for SMITH mmn RINGER in West Ham in the later 1870s, so it seems Olivia RINGER probably married Arthur SMITH.
On FreeBMD there is a birth :
RINGER Flora Lavinia, Mar qtr 1872 West Ham vol 4a p30 (I couldn't see this on the GRO to check the mother's maiden name)
Is it possible that Flora Lavinia RINGER decided to change her name to Florence Olivia?
Could the Olivia RINGER who married in 1873 be related?
No definite answers yet, but it might provide fresh lines to check.
Philip
ADDED - on FreeBMD there are RINGER births in Guiltcross, Norfolk for an Olivia, a Lavinia and several James in the 1850s- so if the Lavinia idea works out, this could be a potential lead