You want to specify our WWW. version in our site because the primary with Google (google has lately transformed all towards the NON www. version as primary).

Therefore we are attempting to specify this will be our .htaccess file using the following in Apache:

#

enable rewrites

Options +FollowSymLinks
RewriteEngine on
RewriteBase /
RewriteCond % ^worldofbooks.com [NC]
RewriteRule ^(.*)$ http://www.worldofbooks.com/$1 [L,R=301]

However, after carrying this out and setting www. as primary in the search engines Website owner tools we still haven't seen a big change.

Any advice or could someone audit the code?

That appears fine except you are not indicating what variable you're matching against within the RewriteCond. What you would like is:

RewriteCond %{HTTP_HOST} ^worldofbooks.com$ [NC]