Hi CivilizedServant
Wow this really is a mystery!!!! Have checked births, marriages and deaths for this lady and her family but have come up with nothing I'm afraid, other than the birth for Albert, which you already have, strange though that she has registered her sons birth and that there doesn't appear to be any obvious entries for her other children. I did find a possible death for a Jane Newman b1832 d1905 Qtr JFM Dist St George Hanover Sq Vol 1a Pg 319.
She gave a maiden name of Perry on her sons birth certificate , however I failed to find an earlier entry in the census using this name combination of Jane Perry b 1833 Bath, which made me wonder whether this was in fact a married name, however could'nt find a marriage to support this theory but did find in the 1861 census RG9 Piece 148 Folio 59 Pg 41 Civil Parish Islington County Middlesex (according to Genuki abt 3 miles from Westminster and St George Hanover Sq, Middlesex)
Alfred Perry Head 34 Somerset Bath Labourer
Jane Perry Wife 31 Somerset Bath Laundress
Sarah A Perry Daughter 9 Somerset
There are also two lodgers in the house by the name of East.
Looked for the family in the following census and found nothing of them as a family unit.
I failed to find anything of the Wheeler connection.
Apologies if you have this already but thought I would post what I have found - good luck!
Regards
Z