Hi Malshie, have been to the archives today, found a christening for Teresa Larkin born 16/12/1915 christened 26th Dec 1915, Godmother Margaret Brown, it states next to her name sames as Josephs, 17th Jan 1926 Ipse confitmatas est ecclest St. Bedow apud Jarrow, did not find a christening for Margaret Larkin. Just as a matter of interest I noted a christening for Maria Betts born 21/6/1915 christened 11/7/1915 of 66 headlam Street mother Maria Betts(godmother of Joseph) Godparents were James Larkin and Julia Larkin(just thought they may be related to you.
Also looked at some documents for the school I mentioned ,Carlisle Memorial,
It opened 1900 and closed 1958. They do have books with names of children, when they started the school and when they left,they went on to St.Mary's when they were 7 or 8. Will go back tomorrow and have a browse through them, I may find your family.
Sheila