On reading the Apache docs, I see that there is a missing ServerName field in my VirtualHost config (i.e. the guide I referenced is wrong). However correcting this and restarting Apache makes no difference. This is the corrected config:
# cat bree.org.uk
<VirtualHost *:80>
ServerName bree.org.uk:80
ServerAdmin pocallaghan@gmail.com
DocumentRoot /var/www/bree.org.uk/html
ErrorLog /var/www/bree.org.uk/error.log
CustomLog /var/www/bree.org.uk/log/access.log combined
</VirtualHost>