Your entitlement to free NHS treatment depends on the length and purpose of your residence in the UK, not your nationality. There may be charges for some NHS services, for example, your dental treatment, and you may be entitled to help with these charges.
Have a look at the excellent website from the Citizen’s Advice Bureau (click) which provides detailed information for people from abroad. For instance, you may be British but live abroad and may not be eligible for NHS care.