The British Museum bought the marbles from Lord Elgin and is the custodian of them. They will need to make decisions about their future. The Prime Minister does not control the future of these statues.
When considering their future the Museum has researched how the marbles were obtained. Evidence suggests that Lord Elgin got the permission of the Turkish authorities who controlled Athens at the time to erect scaffolding and carefully remove some of the statues. The Parthenon was in serious decay and remained at risk. Some fragments were resting beneath the building where they had fallen off. It had suffered from Turkish and Venetian military activity. It would not have been possible to have spent all the time and trouble on removal, transport to the docks and loading onto a ship without the agreement of the authorities. Removing them helped ensure their preservation which was less assured given the negligence at the site. These were large heavy objects that needed careful handling and could not have been stolen or smuggled out.
Athens displays the marbles it owns in a museum and does not wish to put them back on the building. Athens has copies of the marbles that are held in the British Museum and other overseas displays as part of its display of what the frieze would have looked like. So to say it is like cutting up the Mona Lisa is not true. Half of the statues are permanently missing or destroyed from the local wars and lack of maintenance in the past. The other half including fragments are split between Athens, London, Paris, Copenhagen, Munich and Wurzburg . No-one thinks the full frieze exists, nor can it be restored to the building. The British Museum has made clear over the years that these sculptures are an important part of its world collection, properly come by. Athens rightly displays all it can close to the Parthenon along with copies to give visitors there an experience of what the Parthenon looked like before the wars and the lack of care gravely damaged it.