Last night I had to run:
$ sudo apt update && sudo apt install resolvconf
So, I could sensibly connect to the Internet.
Obviously, that was because resolvconf somehow became uninstalled. That deduction came after a fair few hours flapping about. The only conclusion I can come to is that the last $ sudo apt update && sudo apt upgrade removed resolvconf ...
I'm more than happy to run any diagnostic stuff, but I'm unsure how to obtain a transaction history from apt