If you generate your CSR with www.domainname.com then Certificate will protect both http://www.domainname.com and http://domainname.com
This ONLY applies on common name or host-name begins with www. e.g. http://www.domainname.com.
So, if you request certificate for http://www.domainname.com from WebhostUK Limited the certificate will apply on https://www.domainname.com and https://domainname.com