Looking for birth registrations of Edward and Elizabeth Livermore

[LizzieL]

In 1851 Edward Livermore age 13 and Elizabeth Livermore age 3 are with their grandmother Elizabeth Livermore age 70 widow in Swaffham Prior. Grandma was born in SP as were both children.
In 1841, Edward age 3 is living with Daniel and Elizabeth Livermore both recorded as age 60, Margaret Livermore 25 and Elizabeth 15.
In 1861, Elizabeth is living with aunt and uncle James and Margaret Badcock. (Margaret Livermore married James Badcock at SP on 19 May 1855, Margaret's father confirmed as Daniel Livermore, one witness was George Livermore. )
Edward is with his wife and children. Edward married Mary Iveson in SP on 10 Nov 1858, no father listed for either on Freereg transcription.

Elizabeth married John Mann on 13 Oct 1865, she lists her father as Joseph Livermore labourer deceased. But no sign of a Joseph Livermore of a likely age dying in Newmarket district between 1847 and 1865, so possibly he is invented.

Can anyone find birth registrations for these two children, please?

[Milliepede]

Most elusive births aren't they

On the face of it you would think Margaret was possibly their unmarried mother if only she hadn't put Elizabeth as a niece. 
There's an elder sister too Sarah 17 in one of the census but born before birth registration I know.

I guess one thing to do is work through the siblings of Margaret to see who could have mothered (or fathered) them, won't help with finding the birth registrations though 

[emeltom]

Can't see any registration but there is this

Edward Salisbury Livermore baptised 21 Jan 1838 Swaffham Prior mother Margaret (single woman)

Emeltom

[LizzieL]

I don't think Sarah is the sibling of either Edward and Elizabeth (assuming they are brother and sister), I think she is their cousin. Her entry in 1851 says granddaughter and visitor, But edward and Elizabeth are just down as grandson and granddaughter. I may be reading too much into it, but Sarah could be with grandma for just a few days and Edward and Elizabeth living there permanently. I think Sarah is daughter of William and Ann, there is a Sarah bapt in SP in 1832 d/o William and Ann. William Livermore married Ann Willis in SP in 1831. But I haven't yet found William and Ann in 1841
 to see if Sarah is with them.

Thanks for the baptism emeltom, don't know how I missed that, so it confirms Margaret is mother of Edward and might mean a Mr Salisbury is his father.
But Elizabeth is still a mystery, unless Margaret lied about being her aunt. 10 years between the two children makes me think that they might have different mothers.

[LizzieL]

I've found Edward Salisbury Livermore's baptism transcribed as Lovemore, and also Elizabeth's baptism as Levermore on 30 May 1850 at SP - a bit later than expected. Father Joseph occ coachman and mother Sarah Ann.
So there's Joseph again, but did he really exist? Did Sarah Ann baptise her illegitimate daughter at age 3 and invent the father?