My feeling is that the Argentine government needs to feel that they're respected, and their interests treated as legitimate enough for discussion. Given the history of the dispute I'm more than a little sympathetic to this position. But in order to counter this kind of emotional appeal, the British are likely to impute Argentine calls for serious negotiations to the possible revenues involved. Unless the Argentine government is able to seriously disrupt surveying/extraction operations, I don't see the British government becoming more open to changing its policies any time soon.
This is the World of the Theater
3 hours ago