There is no written document in which England or Britain relinquish the right to own the Falklands. The Falklands has been a part of much controversy. However, until a treaty or land is drawn up with the countries who would like to own the Falklands, the territory belongs to England.
Great Britain Went to war over the Falkland Islands. This shows that they have a devotion to the Falklands. If Great Britain did not lay claim to the Falklands then why would its people identify as British? Just today Great Britain stood beside the Falklands saying they will always be ready to support them.