Forgive me for digging up an old thread as I look for ways of procrastinating.

I wonder whether the birth might not more likely be 1933 Hammersmith (late in the year so in early 1958 he would have been 24).
It's possible he may be living, so just go to
http://freebmd.rootsweb.com/cgi/search.pland search for that birth. There are other births with the same mother's surname in Fulham 1929 and Brighton 1936, and later births in Essex and Middlesex, but other than that all births with those surnames are in quite different places. There are also marriages that match the Brighton and Hendon births better.
Unfortunately, there is no marriage I can see that is a good match for that 1933 birth.
For marriages of Charles Birch, his father ... was he Charles Austin Birch as well, from the marriage certificate? Likely not, unless he was born after 1911 when only middle initials show in the births index. But even if so, there are so many Charles A Birch marriages; if it had been a second marriage for the mother of Charles c1933/4, her surname for the marriage would be different from her surname on his birth certificate.
I would really get that birth certificate so you can rule that birth in or out.
That said, the birth and marriage suggested by Maria match well too. I'd say close your eyes and order one of the certificates to start and see how it matches.

(edit - Jan contacted me by PM and I offered to do some more digging if she decides to get those birth certificates. I'm stymied so far!)