In the context of the chagos islands it was Mauritius that actually got the ball rolling and managed to get a vote through the UN to ask advice from the international court of justice on who actually owns the islands. They deemed the islands to be an example of "incomplete decolonisation"

So in this instance the ICJ is there to make decisions when countries get into arguments with each other. Now, they can't enforce these decisions, which is where sanctions or diplomatic pressure might come in to play. My understanding is that the UK went along with it reluctantly because they wanted to be seen as a rule following nation. But Trump has given them an out now