Hi folks.
Wow! You've all been very busy! I really appreciate the work everyone has put into this question. Here's what I've found in the last 24 hours:
Elizabeth Halliday:
Durham Online
Baptism, Chester-le-Street District – Record Number: 468199.0
Location: Chester-le-Street, County Durham
Church: St. Mary and St. Cuthbert
Denomination: Anglican
22 Oct 1848 Elizabeth Ann Halliday, of Plawsworth, daughter of George Halliday (Cartwright) & Phoebe Ann Halliday (nee Hodgson)
GRO
Halliday, Elizabeth Ann (Mother’s Maiden Surname Hodgson). Reference: 1848 S Quarter in Chester-le-Street Volume 24 Page 43
This unfortunately doesn't match Elizabeth Sherlock's 1848 birth certificate (see attachment).
In the 1851 census Margaret Dial is recorded as aged 1, birthplace Berry Edge, and presumably her mother (Sarah Dial, aged 25) is recorded as a visitor in the house of Matt Snowdon (Residential Note: Lead Gate).
According to Peter Dial and Isabella Sherlock's marriage certificate her father's name was Thomas (surname Shawlock on the certificate). The 1841 census shows Isabella's parents as Thomas and Elizabeth. One of her siblings is George, born in 1832, who appears to have been one of the witnesses at Isabella's wedding in 1850.
I've spent several hours combing through DTO and GRO searches and not really come up with any definitive solution. The birth certificate has no father named, which is usually a strong indication that the child was illegitimate. The 1851 census shows Robert, Isabella and Elizabeth living at Willington. The Halliday link is credible and it's a line I definitely need to further investigate, but I guess I'm hamstrung by the lack of any proof like adoption papers (not that they existed for most people in those times). If I find any more information I will post it.
Thank you to everyone who has put in so much effort to find out new information. This is a fantastic site that has many brilliant contributors such as yourselves. I really appreciate your help.
Peter