If you wanted to bind it to the Falklands you'd be better off doing it in 1777 when the British first got involved there. By 1833 it's somewhat too easy for the British to get turfed out, especially as I seem to recall the Argentines made their own Patagonian colonies, mainly to control the Cape, around the same time. So did Chile, actually, hence the border down there. Much easier to do it a bit before, while it's still under Spanish control, as you can either use a war to grant the area de jure to Britain, or you can use the danger of war to prevent the Spanish turfing the colonists out themselves.
I must admit, British settlements in, and ownership of, the Cape has often intrigued me. It was the British theory that control of the world's oceans and maritime movement could be achieved by the strategic control of five locations: If I remember, they are Gibraltar, Singapore, Cape Horn, the Cape of Good Hope/Cape Colony, and I think the other was the Suez, though I think this theory predated the Suez Canal so I'm uncertain. Similarly I wonder about Britain controlling the Panama Canal. Could have some interesting repercussions...or alternatively may make little difference whatsoever.