Sophos blocking all web browsers, can't use internet

All my web browsers stopped working last night, can't connect to anything. Everything else that connects to the internet is fine.
Uninstalling Sophos fixed it, reinstalling made it happen again. I thought I'd switch to Avast so I uninstalled Sophos using the uninstaller but Avast says it's still detecting Sophos and won't install. Gah!

Any ideas what I can do here? I'd like to either get Sophos working again (ideally) or at least get it properly off my machine so I can install something else.

Also, I didn't change anything on my computer last night, so I have no idea what caused it.

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