Solution:
Open your Apache conf file:
sudo vi /private/etc/apache2/httpd.conf
…and relax the permissions somewhat by commenting out (with a #) or removing the ‘deny from all’ line:
<Directory />
AllowOverride None
Order Deny,Allow
# Deny from all
</Directory>
With thanks to Damon Parker. See his site for an explanation of why you need to fix this in the first place.