How can I disable Internet access for programs running in Wine?

Wine uses an equivalent of the Windows registry, accessed through regedit as with a normal Windows system. I would imagine there is a key buried in there somewhere that you could use to disable the network connection, or at least make it local-only. (I'm not an expert on the Windows registry, so I can't say where unfortunately)

Alternatively, You could try setting Wine to use a proxy to access the internet, which would obviously fail if the proxy you specify doesn't exist. That is a bit of a hack though.

You can try using firejail. For example:

firejail --noprofile --net=none wine iexplore

Look for error messages in the terminal to see that internet is not working.

0009:fixme:urlmon:InternetBindInfo_GetBindString not supported string type 20
0009:fixme:ieframe:handle_navigation_error Navigate to error page