I passed on the details about FollowsynLinks ans FileInfo directive to the host, who responded:
We’ve added a few lines to your .htaccess file try again.
Here’s what they added:
# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>
# END WordPress
It seems to have done the job!