The problem is solved. I was getting mixed up between the password associated with my Apple ID, which is not the one I wanted, and my Machine Password associated with my Admin account that I set up when the OS was first installed, which is the correct password to use for Homebrew.
I have a further problem now in that my terminal window is seemingly stuck with the message "Downloading Command Line Tools (macOS El Capitan version 10.11) for Xcode" - I guess it's just a long download... I've just had to enter the password again, and it's just come up with an error...
/usr/bin/sudo /usr/bin/xcode-select --switch /Library/Developer/CommandLineTools
xcode-select: error: invalid developer directory '/Library/Developer/CommandLineTools'
Failed during: /usr/bin/sudo /usr/bin/xcode-select --switch /Library/Developer/CommandLineTools
Any ideas, anyone? Thanks.