They can claim stuff, getting it back may be tricky.
The British Museum is governed by a specific UK law, and in 2005 they were sued by the UK Government to block them from returning looted items in their collection on the basis that they had no legal authority to do so.
There are plans to change that, letting Museums including The British Museum return items on “moral grounds”, [but it looks like those changes have been stalled by the Government](https://www.museumsassociation.org/museums-journal/news/2022/10/government-delays-bill-allowing-nationals-to-return-items-on-moral-grounds/).
Returning items to other countries is a controversial topic in the UK, and generally the current Government’s supporters are on the nationalistic/imperialistic side.
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