Ok, Murphy's Law, just worked it out after posting the question!
The extra condition needed for the Wordpress rewrite is:
RewriteCond %{REQUEST_URI} (/|\.htm|\.php|\.html|#.*|\?.*|/[^.]*)$ [NC]
So the complete Wordpress rewrite code becomes:
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_URI} (/|\.htm|\.php|\.html|#.*|\?.*|/[^.]*)$ [NC]
RewriteRule . /wordpress/index.php [L]
Now I'll go finish my humble pie.