To delete a free hosted WordPress.COM blog you must be logged in under the exact same username account that registered a blog to delete the blog. To prevent accidental or inadvertent deletion of blogs, there are multiple warnings given that blog deletion is permanent and irreversible. Lastly, a verification link is sent in an email and must be clicked to delete a blog. If clicking that link does not work then copy and paste it into your upper browser window and click.
Deleted blog URLs are not recycled, regardless of who registered and deleted them and no exceptions are made.
Alternatively, to change blog visibility to private go to > Settings > Reading scroll to Blog Visibility and choose option 3 . See the guide here http://en.support.wordpress.com/settings/privacy-settings/
IMPORTANT NOTE: Deleting blog content and deleting blogs does not remove any indexed content from the SERPs (search engine page results). Google and Bing only clear their caches of deleted indexed content that produces a 404 (page not found) every 3 - 6 months.