My inclination would be to fall on the side of the British - as they were the legal authority. Obviously, this has to be taken case by case. But let's say hypothetically, that a great Australian Aboriginal treasure was lifted by the British prior to Australia's Federation in 1901. I don't believe Australia would be justified in demanding the return of those artifacts.
The marbles were different because this was a case of outright theft. The British government was not in control of Greece, Lord Elgin was not acting on behalf of the Government, but on his own. It became a British Government problem when the British took it upon themselves to condemn Elgin, then bought the marbles from him at a reduced price. It has remained a British Government problem ever since when members of both parties have campaigned and pledged for the return of the marbles, then nothing happens.
Any visitor to the British Museum can see that the Marbles would look better at their place of origin,
I profoundly disagree. Nothing beats seeing an item better than in its original context. Because the marbles were hacked up and now displayed in doors, we loose the drama of them in the context of the Parthenon, and its natural lighting. Who knows? Maybe there were cetrtain pieces that were oriented in such a way as to catch the morning light.
What the British could do is remove the marbles, return them to the Greeks, then in the space where the marbles (and Elgin's loot) is, convert that into a Virtual Reality museum. Visitors to the museum pay $5.00, for VR helmet and experience what it would have been like waking through the Parthenon in Ancient Greece. The Brits could claim that the original is in Greece, but they have the technology to bring the feeling of the original to life.