How can I connect to IMAP (for example imap.gmail.com) in Outlook from behind a HTTP proxy (no authentication needed) ?
IMAP is a different protocol and uses different ports than HTTP. The standard ports for IMAP are 143 and 993 for secure IMAP.
If you have problems connecting, I suspect that your firewall/router is blocking the IMAP port(s).
The HTTP-Proxy can support the CONNECT method to allow ssl. Using it you can connect to port 443 anywhere. The question is whether your proxy allows other ports. 25 is usually blocked because of spammers.
I think telnet proxy port CONNECT imap.gmail.com:993
If it is rejected, bad luck.
Otherwise download socat and point your client to 127.0.0.1:993 and let socat forward that local port towards gmail using the PROXY function. socat can do what you need. I can give a command line if you need it.
several utilities can be used to trick a https proxy to forward arbitary data, for example: