Have a plan of what to do next

Whether or not your loved one is receptive to what you are saying, it is important that anyone suffering from an eating disorder is under the care of a doctor.
Arrange for your loved one to see the GP. If they are over 18, offer to go with them as support, or to talk to the GP in case they are too embarrassed.
If the GP is concerned that your loved one may be displaying signs of an eating disorder they will most likely make a referral into CAMHS (Child and Adolescent Mental Health Service) or to the Eating Disorder Service. Or alternatively they might want to monitor your loved one for a while.
If you are not happy with the plan your GP has given you, do not be afraid to say so. You know your loved one best, and parents/carers often have to fight on behalf of the sufferer.
The alternative to being seen by the Health Trust is to pay for your loved one to see a private counsellor or therapist. Talk each of these options through with your loved one, and try to come up with a plan which suits both parties.