It's about a 10 day hop over to Simonstown, so very do-able if inconvenient. Any vessel capable of getting to the Falklands and operating there should be up for it.
Desire Falkland Oil Find May Fan U.K., Argentina Feud - BusinessWeek
With the very good news of a second oil strike in the Islands, we need figure out how we get our oil off the islands and back to Britain. The answer is simple. The islands have a perfect deep water harbour at San Carlos Water. We just to establish an oil storage facility there and send tankers into it to ship our oil to friendly refineries.
From an aviation point of view, just imagine the traffic going into and out of MPA to support this. The Falklands would become the richest nation in the world per capita.
Don't cry for me Argentina