If you are a Commonwealth Citizen and you can prove that a grandparent was born in the UK you can apply for UK Ancestry Visa.
You must, however, be planning to work in the UK and may have to pay the health surcharge, which will entitle you to treatment through the National Health Service.
With a UK Ancestry Visa you can stay in the UK for 5 years and can then extend it or apply to stay in the UK permanently.