No one in England even cares about this. It's literally just the government making random arguments up to throw at the right wing groups, it's all political. Pretty much everyone would be absolutely fine if we gave them back.
The only people that care about any of this are basically fascists anyway and they won't go and look at them they just want no one else to have them.
Even if they had permission from the Ottomans - it's beyond meaningless.
It's like arguimg Britain had permission from France to take [random African artifact located im a French colony] and therefore any and all claims by the affected country are now void.
The Brits are claiming that they had permission of the sultan, the governor and the city of Athens. However somehow no documents proving any of that are available in Turkey or Greece.
However Athens was part of the Ottoman Empire for 350 years and they had a lot more influence over it, then France had in Africa. It really is more like the Tsar giving permission to sell some mosaics from the Saint Sophia Cathedral in Kyiv.