I panicked about this about six months ago (looking for any and every reason why I wouldn’t be indexed!)
While it’s true that canonicalization issues can cause duplicate penalties, sometimes your host will allow access with or without www. It’s not that you have two identical sites, just that your host re-routes traffic to the same site.
If your host does that (mine does) it can seem like a problem when in fact it isn’t – but you’re right to check with your host.
This is what they told me:
fortunepalace.co.uk is your domain, http://fortunepalace.co.uk and http://www.fortunepalace.co.uk are both valid URLs to enter the same site that you have uploaded and both display the same content.
Since then, Google has indexed me fully, so I’ve stopped worrying about it!