On 29 April 1980, British police assured Iran that their embassy was secure. The very next day, terrorists stormed the embassy and took 26 hostages. With the Iranian government willing to let the hostages become martyrs, and the British government only willing to talk if the terrorists surrendered, 26 lives hung in the balance.
In 1982, the average Briton didn't know the Falkland Islands existed, let alone their status as a disputed British territory just off the coast of Argentina. That changed when the Argentinians invaded the islands and overwhelmed the small defending force. Both nations claimed the islands were theirs, but now Argentina thought the British would give them up without a fight. They were wrong.