It might not have been as it was still early days as far as registration was concerned.
I checked the full index 1838-1840 but could only find the Tynemouth one

Is it worth asking the local office (it would be Newcastle now) to do a search - Ann Lowther 1838-1840, father William, mother Mary? Sometimes names get missed off in the transfer between the local office and the quarterly national returns.
Gadget