Hi
Constance was born Dec quarter 1902 registration district Wellingborough
You need to search Freebmd
http://www.freebmd.org.uk Wellingborough to see if you can find a birth, followed by a death of a child. If they married in 1900, I would think Constance was their first child, so you need to search after that, discounting the time allowed for Arthur.
It might be difficult though, as at a quick glance I've found at least two it could be:
Annie born March quarter 1907 died March quarter 1907
Annie Elizabeth March quarter 1907 died March quarter 1907
Your only other hope is that someone has access to baptism records where it will give parents' names.
Jan
Jan