If you look at FreeBDM

and type in births of HAWKINS and Mother's Maiden Name: AVERY - you'll find

December Qtr 1920 - Hammersmith
Robert A HAWKINS

and

March Qtr 1921 Newton Abbott
Queenie L HAWKINS

and then again..... if you go onto Genesreunited, you'll find these names listed, and names to contact..... keep you busy

I think it's starts about the Middle of 1911 when the mother's maiden name is listed on the birth records (FreeBDM) - before that, it's just the birth surname.