Looking at it, Elizabeth’s mother Harriet Chapman, née Smith, was a widow when she married William Carr. That marriage was only in 1866. Elizabeth would have been at least 10 years old then. It’s possible she might not have used the name Carr when she registered the birth, although I’m having problems finding it using Chapman as well…!

Hi Denise,
Thank you so much for the information. I looked at the baptism for Thomas Carr and feel this could be the correct one due to address given on birth certificate for next child Ellen being same address.
Big Thank you

Hi Heather,
I have purchased digital copy of birth for Elizabeth Carr giving mothers maiden name Smith. It states William Carr as father and mother Harriet Carr of late Chapman, formally Smith.
looking at 1861 census there is a Sarah Carr she is baptised same time as Elizabeth 1863 but named Sarah Chapman daughter of William and Harriet Carr aged 10 years. I have searched Gro for Sarah but cant find her under either surname. Definitely mind blowing especially with Harriet not marrying William until 1866.

There’s a birth for a Sarah Chapman Q4 1852 Sheffield with MMN Chapman. That might be her? I see that Sarah married as Carr in 1870 though, giving her fathers name as William Carr, scissor grinder.