When I set up eM Client I chose my own avatar (in Settings, Accounts), however I now want my avatar to match our website favicon. Is there a way to disable the avatar I’ve set and force eM to use the favicon image?
The account avatars do not update from Internet the same way as contact avatars do. It is initially set from the favicon when you add the account, but if you want to change it after that, you will need to go to Menu > Accounts and click on the avatar, then choose an image from your device to replace it.
Thanks for confirming. Is there no way to revert to the favicon once it’s been manually changed then?
If there is, unfortunately, no possibility to update the account avatar automatically, can you download the avatar / new favicon as a picture file and add it manually in the account settings? 
No, account avatars are only sourced from the Internet at the time you setup the account. They are never updated automatically after that.
Yes, just go to Menu > Account and click on the avatar, then choose you own image to replace what is there.