What options? The Junta invaded sovereign territory ffs
There were none. No realistic options, at least.
The limits on Britain's ability to act were quite serious. The choices were really:
1) Send a Task Force, reoccupy the Falklands, declare victory.
2) Send submarines, blockade the Falklands, force the Junta to withdraw. This would be a very long shot, not least because Britain would be effectively starving the Islanders as well as the Junta's troops.
3) Demand the Junta withdraw, with the Falklands occupied by an international UN force. This would be a sign of weakness, even if the issue was agreed in Britain's favor. It probably would not have been. The Junta tried hard to portray the issue as a 'colonial' one and, if the UK looked weak, the UN would probably side with them.
4) Demand the Junta withdraw, or else. Which begs the reply of 'or else what?' Go to 1.
5) Use nukes. No one in their right mind would try this.
6) Surrender the Falklands, abandoning the Islanders to a very hostile regime.
The bottom line is that the time for talking ended when the Junta landed troops. There was no longer any room for a solution that didn't end with Britain repossessing the islands.
Chris