Okay, it seems that this was a permissions issue, but a different one to that described by @Cătălin Stan.
I was (incorrectly, as I now understand) using brew with sudo, probably because I was getting permission issues when I tried to brew install
anything. However, it seems that brew is supposed to run without sudo. Doing this eventually led me to
and alerted me to the fact that I might have permission and/or ownership issues effecting brew. Running sudo chown -R
whoami/Library/Caches/Homebrew/
fixed these, and MySQL installed perfectly.