Thanks for your responses. Yum is not an option as I'm on a machine without root privileges.  

OK, so I have to be a bit contrite here, I tried everything you suggested, but in the end the solution goes back to this comment, and the LDFLAGS environment variable:

https://bugs.python.org/issue34028?@ok_message=msg%20355232%20cr%C3%A9%C3%A9%0Aissue%2034028%20message_count%2C%20type%2C%20versions%2C%20curieux%2C%20nosy_count%2C%20messages%20modifi%C3%A9%28s%29%20avec%20succ%C3%A8s&@template=item#msg339455

I think I was using the wrong compiler when I tried that solution the first time.  So I'm sorry about that.  

But while we're here, I may as well ask if there isn't another way to do this, without having recourse to the environment variable.  Is there a way to specify these flags using just the configure script?  Based on something I read somewhere on the web, I generally prefer to steer clear of setting environment variables, though perhaps I needn't be so reluctant.  Incidentally, the environment variables OPENSSL_LDFLAGS etc as suggested in config.log (thanks for that, I wouldn't have thought to look there) do not appear to work.