WordPress pages break with custom permalink settings (theme directory not output)

This was resolved with the help of @AndyMacaulay-Brook

The htaccess had some incorrect (non-wp declarations) which when removed solved the issue:

<IfModule mod_rewrite.c> 
RewriteEngine On 
RewriteBase / 
RewriteRule ^index\.php$ - [L] 
RewriteCond %{REQUEST_FILENAME} !-f 
RewriteCond %{REQUEST_FILENAME} !-d 
RewriteRule . /index.php [L] 
</IfModule> 

# BEGIN WordPress 
<IfModule mod_rewrite.c> 
RewriteEngine On 
RewriteBase /wp/ 
RewriteRule ^index\.php$ - [L] 
RewriteCond %{REQUEST_FILENAME} !-f 
RewriteCond %{REQUEST_FILENAME} !-d 
RewriteRule . /wp/index.php [L] 
</IfModule> 
# END WordPress 

Removing everything outside of the WP declarations fixed the issue