You're not looking in the right places. Births, marriages and deaths can be found at http://freebmd.rootsweb.com/cgi/search.pl
Using this I located a birth registration for Annie E E MAY in the Redruth district Dec qtr 1918 vol 5c page 242. Mother's maiden name PHILIP.
FREEBMD also brought up the name of a son born to them (put WARREN in the main search field, MAY in the mother's surname field and select Redruth in the district drop down box). I won't put his name on here as he may still be alive and there is a privacy rule in England.
Going back further you will find http://www.cornwall-opc-database.org/
useful, but in order to do that, you need to obtain some birth certificates using the references from FREEBMD.