Yes, NRIs can get health insurance for their parents and other family members who live in India. If you are an NRI, you can select from a range of health insurance policies, including critical illness coverage, family floater plans, and senior citizen health policies, based on their individual needs.
In addition, NRIs can purchase a healthcare policy that will pay for their parents and their own medical bills in India. Unless the contract specifically states foreign coverage, health insurance companies usually limit their coverage to medical costs spent within India.
Medical costs incurred abroad, however, might be covered by travel insurance, but only if the policyholder becomes ill while travelling. Therefore, health insurance acquired from an Indian insurer will not cover the expenses incurred if an NRI living in the UK (or any country other than India) needs medical treatment there.