Thank you Wivenhoe, but I have this information. If you know more or have suggestions about Ann before she was married or Ann and Elizabeth's parents, that would be really helpful.
My working theory is that the parents are Peter Manning and Eleanor Creden (or Creedon/Creed/Craden/Grad in other sources. It could actually be Creighton for all I know). Ann gave her fourth child the middle name of Eleanor, so maybe after her mother. Peter and Eleanor married at Saint Magnus the Martyr in the City of London on 19 Apr 1813. He was a bachelor and she a widow. Creden is probably her maiden name, but could be the name of her first husband, depending on how you read the Latin in Ann's (Maria Anna's) baptismal record, from St. George's Cathedral in Southwark:
"Die 15 Jan: 1814 nata et die 27 Feb: 1814 baptisata fuit Maria Anna filia Petri Manning & Helena olim Creed, conjugum Sponsores fuerint Petrus Giller & Catharine Certon”
I read olim Creed to mean her original (maiden) name was Creed (or whatever variant). Petri and Helenae are just the Latin genitive forms of Peter and Helen and Helen is surely the cleric's Latinization of Eleanor.
Assuming this is correct then there was a sister Honora born in 1815 and baptized at St. George's (Catholic) cathedral. Elizabeth was born in 1818 and baptized in Bermondsey Dockhead, also Catholic. After that I only have theories about Peter and Eleanor. I assume he is alive at the time of time of Elizabeth's wedding in 1841 and I'm pretty certain he's dead by Ann's second marriage in 1860. There was no legal requirement to indicate whether a father was alive or dead on a marriage record, but it seems unlikely that he would be called "dead" in 1860 if he wasn't. It is possible he was also deceased in 1841 and it wasn't noted. Peter is not a witness to the 1841 wedding. He's not mentioned at all on Ann's marriage record with Reuben Smith in 1834 in St. Mary Newington (C. of E.).
There was a Peter Manning who died at the age of 80 in March 1846 of "natural decay". His wife was named Sarah, so if it's him then Eleanor is probably dead and he's remarried. Divorce was apparently really rare back then and cost a lot. The only plausible record of a Peter Manning in the area with a wife named Sarah is a marriage record between Peter Manning and Sarah Sherricks in Whitechapel in 1843 except that the Sarah Sherricks in Whitechapel in the 1841 census would be ~23 years old and he'd be 77. Not likely.
I don't know anything about Eleanor. A sponsor at Honora's baptism was "Honor Creedon", which should be a clue. There was an Eleanor Manning who died in Walworth, Southwark in July 1843 but her record of death doesn't mention her marital status and the death was witnessed by "Mary Ann Cambridge", not a husband. The record does not say that "Mary Ann Cambridge" is her daughter, which would blow up all my theories, but it's a possibility. This Eleanor was 52 when she died, so born ca. 1791, which would make her 23, 24 and 27 when she had Ann/Mary-Ann, Honora and Elizabeth. If they are indeed her kids. That's reasonable. If Peter was the guy who died in 1846 he'd have been 48, 49 and 52. That'd make for a big age gap with his wife.
There is an Honora Manning who was admitted to the Fulham Road workhouse in 1884, who is described as R.C. (i.e. Catholic). She'd be 70 although the workhouse record suggests she was 66. She was admitted from St. Margaret's parish, which I assume is the one near Westminster Abbey. She apparently didn't marry, so I don't see a record that mentions her parents other than her baptismal record.
So as well as the question from my previous post I have a lot of conjectures. I'd sure appreciate anyone's thoughts on any of this.