The argument I've been trying to make so far, which has either been misinterpreted or misunderstood is this -
The UK has been satisfied with opting for convenient choices over idealistic ones for decades if not centuries, including but far from limited to the depopulation of the Chagos Islands. It is a part of a club of countries that enjoy sole rights a few things today, like nuclear weapons and a veto in the UNSC. And its indicated a willingness to use force to ensure that those rights remain an exclusive preserve of this select group of countries. Rights that were granted for no other reason than the fact that it was a powerful country.
This isn't a criticism of Britain, its just an illustration of the fact that it is no stranger to realpolitik. And it would not be uncharacteristic of the country to opt for a pragmatic solution to the dispute rather than chase after moral high ground.
This is also why Mr Cameron's dispatch of diplomatic delegations to South American capitals to 'explain its position' is probably a wasted effort, because there is no misunderstanding involved, on their part.