For better or for worse the decision has been made at Google Chrome and it seems also Mozilla Firefox, that to access the microphone and web camera from their browsers, the website must be running under SSL (ie https).
This has been slowly coming, and since around 2015 HTML5 audio and video recording could only be done via HTTPS. Now however, with new versions of Chrome and Firefox even Flash based recording requires HTTPS. Flash is granted access to the microphone and web camera by the browser, and in this case it is acting as the gatekeeper.
To be fair this is probably a good idea. Some malware has been monitoring voice and video and in general we don’t want it snooped on.
You can test audio and video recording on https over at https://demo.poodll.com . If it works there for you with Google Chrome, but not on HTTP at your own site, then its a fair bet that you are going to need to implement SSL.
Its actually not clear which versions of Chrome and Firefox the line is drawn at, and for many users it seemed to happen suddenly. Presumably this is because of an automatic browser update. But its not going away and if you are not on HTTPS you should move to HTTPS quickly. This article also talks about Google’s push on HTTPS
If you are not on HTTPS, and even if you are not experiencing problems, you should set it up now. Moodle explains here about that: https://docs.moodle.org/33/en/Transitioning_to_HTTPS
Many users have reported success with the free SSL certificates available from : https://letsencrypt.org/
That is an inexpensive option and we use them ourselves on some sites.