Would sinking both Argentine capital units have been politically costly?

What political liability might Britain have faced if its forces had sunk both major Argentine naval units?

Britain could use superior force, but destroying both units might have looked disproportionate and weakened its claim to be acting with restraint under the international order.

Destroying both General Belgrano and Argentina's carrier could have appeared excessive even if Britain possessed the military means. Military superiority did not remove the political need to show proportionate restraint. The Vulcan missions over the Falklands demonstrated that Britain could reach the islands and implied a wider striking capability. Bombing the Argentine mainland, however, risked diplomatic trouble at the United Nations and could have weakened Britain's claim to defend the international order.