There are 234 Edward ... Fawcetts born between 1907 and 1947; of these 29 are Edward only but none were born anywhere near Cambridge.  So, there are no means of identifying his birth from the birth index records.  Same problem with the 1939 census, though if he is still alive his data would not be visible.

Their children were born in Cambridge.  There are no Edward Fawcett deaths in Cambridge up to 2005 when the records cease.

I give up!  Though their marriage certificate would give his age and thus birth year and his father’s name, possibly leading to some birth record.
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Their marriage index, the pnly one for a margaret Drane in Cambridge:

First name(s) MARGARET
Last name DRANE
Marriage quarter 3
Marriage year 1955
MARGARET DRANE married one of these people
Edward S Fawcett
Spouse's last name Fawcett
District Cambridge
County Cambridgeshire
Country England
Volume 4A
Page number 561
Record set England & Wales Marriages 1837-2005
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