There's some kind of DNS error on my small clients website that's located by HeartInternet. For whatever reason the website doesn't appear unless of course www. is specified clearly.

Works: http://www.elmhaven-marina.co.uk

Does not Work: http://elmhaven-marina.co.uk

Just how can this error be fixed?

You'll need a "@" An archive pointing to elmhaven-marina.co.united kingdom inside your DNS

The DNS record simply does not come with an entry for "www." then. It requires a CNAME pointing "www." to "@", meaning, an alias for that raw domain.