I'll step you through how to go about finding Charles' parents:
I went to
https://www.freebmd.org.uk/cgi/search.pl and searched for Charles Bingham b. 1935. There was one result: Charles Henry Bingham, mother's maiden name Chaplin - birth is registered in West Ashford District, Kent, September quarter 1935 Vol2a/1678
(note - this is the civil registration birth index which goes back to 1837. On freebmd, you can access mother's maiden names from 1911 onwards, otherwise the GRO website has the earlier maiden names)
I then searched freebmd again, this time for marriages - of Bingham to Chaplin. I found a record for George H Bingham married to Dorothy M Chaplin June quarter 1935, Tenterden Vol 2a/2968
Because of the time period, another good resource to check is the 1939 Register
Just as an aside, Charles' wife Ruby should be listed by her maiden name, rather than her married name (Charles H Bingham and Ruby B Best, married March 1968, Maidstone, Vol 5F/1219)