Your post made me look at my own installation of Webmin. I was using only http: as well. If you go to Webmin-->Webmin Configuration-->SSL Encryption I generated SSL keys and stored them. Once done, I was prompted if I wanted to swith now, I said yes, I was dropped in http: mode, and had to sign in https: That was it...
BTW, I also took the time to limit the IP addresses Webmin will listen to. (under IP Access Control). Since my boxes are on a 192.168.x.x private network, I limited the IP addresses to that, plus localhost.
Hope this helps.
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