By sheer coincidence, the Saturday before this blew up was the date of a particular art history conference in London, at which there was a talk by Jacques Schumacher (who is the Provenance Curator at the V&A) which discussed the state of affairs around restituting looted objects.
The key obstacle Mr Schumacher highlighted in his talk was, basically, the law. The law that covers disposal of objects in a museum's collection (including restitution) is the Heritage Act 1983, which effectively states that no item can be given away unless the item is an exact duplicate of another in the museum's collection (so a modern 3D copy wouldn't count), or the item is unsuitable for exhibition (which means that the museum has to be legally certain that nobody, student or teacher, present or future, will ever have even the slightest interest, for research or any other purpose, in that object. Obviously this is a very high threshold), or some kind of exchange is involved (he didn't go into much detail on this, but I think the items have to be vaguely equivalent), or the item is rendered useless due to damage. This means that a restitution request, or the fact that the item was looted, is not enough, under the terms of the Heritage Act, for the item to be returned.
There is one exception to this - art that was looted by the Nazis can be freely returned to its country of origin.
The reason that the fact that the item was looted is not in itself enough for the item to be restituted. Mr Schumacher explained that, during the war in Ethiopia in 1868, the British troops brought a dedicated art curator to steal or buy culturally significant pieces at a knock-down rate, to be sold for a much greater price at auction. Over 60 pieces were bought by the V&A museum to educate the public on Ethiopian metalwork. A restitution request from the Ethiopian government has been made, but only in relation to two of the pieces.
Mr Schumacher concluded his talk by talking about a recent resolved restitution request from the Turkish government in relation to a small sculpture of the Head of Eros. This broke off a sarcophagus discovered in what is now Turkey, and was stolen by a British collector and presented to the V&A. In the 1930s, a visitor to the museum recognised it as being similar to the several almost identically carved heads that were still on the sarcophagus, which was by then being displayed in Turkey. This prompted a restitution request from the Turkish government, but then WW2 started and the restitution row was forgotten about.
In 2010, the Turkish government made another restitution request in relation to the piece. By this stage it had been in storage for 40 years, as it was a tiny little carved head off a much larger object that it made very little sense to display out of context. However, because of the very restrictive nature of the Heritage Act, it still couldn't be transferred. The only legal option was sending it over on long-term loan, which was refused by the Turkish government.
The impasse was eventually broken by the Director of the V&A, Tristram Hunt (the former MP), who had the idea of transferring it over as what he called a "renewable cultural research partnership" - i.e. it wasn't legally a restitution, so the head could be reunited - properly - with the sarcophagus without issue. However, the eventual transfer and partnership was conducted during what Mr Schumacher called a "very turbulent time in UK politics" - i.e. Liz Truss. He stressed that the unusual thing about this state of affairs was that it was an open-and-shut case - the looted piece was in storage, there were no plans to take it out, and it made little to no sense without the sarcophagus. The Elgin Marbles are less of an open-and-shut case simply because they aren't in storage!
In terms of whether the law can be changed, Mr Schumacher added that the Tories have no interest in changing the law to make restitution less of a perpetual stand-off, and that he saw little to no likelihood of the situation changing under Labour - bigger fish and all that. Whether the rekindling of the Elgin Marbles row will change this, I don't know.
I hope this helps to clarify the situation surrounding the Elgin Marbles - I'm no expert on this, but I do have my notes from this talk by an expert and I thought it might make a useful addition to this discussion. I don't think the talk is available online if anyone does have any further questions, but I will have another look.
