Once British ground forces had landed at San Carlos, Hamilton deployed with his SAS Squadron 40 miles behind the enemy lines to observe the main enemy defensive positions at Port Stanley, his leadership proving instrumental in seizing this ground, from which the final attack on Port Stanley, which would bring the war of liberation of the Falklands to a victorious conclusion, would ultimately be launched. On 27 May 1982 he identified an Argentine probe into the squadron's position and in the ensuing fight captured an Argentinian prisoner of war. The next night his troop held off another enemy attack, in doing so enabling 42 Commando Royal Marines to fly in to reinforce the position on 31 May 1982, which was a key stage in the Falkland Islands campaign. On the following day his troop ambushed another Argentinian patrol, capturing five members of it, three of whom were wounded.
On 5 June 1982 Hamilton was deployed in command of a four-man observation patrol into positions behind enemy lines on West Falkland to observe Argentinian activity at Port Howard. The patrol established itself in an observation post on the high ground of a ridge called Many Branch Point 2,750 yards from the Argentine positions, from which radio reports were dispatched. In the late morning of 10 June 1982, Hamilton and a radio operator were manning the post when they were discovered by a four-man Argentinian patrol from the 1st Section of the 601 Commando Company, operating out of Port Howard. Fonseka first engaged the enemy force in the open, followed by Hamilton from the post itself. As the small arms fire-fight continued with grenades being exchanged, during which Hamilton was hit in the arm by a rifle bullet, Hamilton ordered that they should both attempt to fight their way out. As the only withdrawal route available was to the rear, and was exposed to enemy observation on the up slope of the ridge for 50 yards to the summit, Hamilton maintained automatic covering fire from within the post at the Argentinian commandos to allow Fonseka to withdraw first in a co-ordinated fall-back manoeuvre. Hamilton then attempted to follow, in the process was struck by Argentinian rifle fire and killed, Fonseka being afterwards taken prisoner of war. Hamilton's body was buried with military honours by the Argentinian garrison on West Falkland, the grave lying in the small cemetery at Port Howard. When the Argentinian Commander of Port Howard, Colonel Juan Ramon Mabragana, was interrogated by the British Forces after the Argentinian surrender on the Falkland Islands a few days later, he stated that Hamilton was "the most courageous man I have ever seen" and recommended that he should receive a gallantry decoration for his actions during the fire-fight. Hamilton was subsequently awarded the Military Cross posthumously.
Subsequent events
The Argentine commando patrol commander from the engagement, José Martiniano Duarte, met Hamilton's wife in 2002 at the Argentinian Embassy in London, expressing his personal regret for the events that had occurred at Many Branch Point 20 years before that had claimed her husband's life, and praising his bravery.
