[PaulRobinson]

No, they can't. The legislation[0], does allow them to lend things out, but:

    The Trustees of the British Museum may lend for public exhibition (whether in the United Kingdom or elsewhere) any object comprised in the collections of the Museum:

    Provided that in deciding whether or not to lend any such object, and in determining the time for which, and the conditions subject to which, any such object is to be lent, the Trustees shall have regard to the interests of students and other persons visiting the Museum, to the physical condition and degree of rarity of the object in question, and to any risks to which it is likely to be exposed.

Lending it indefinitely is not in the interests of students in the UK or other persons visiting the British Museum, and there are considerable risks of non-return. It would be considered a disposal. Disposals are not allowed apart from under certain conditions expressed in clause 5 of the Act.

Politics is focused on more important matters, but the law is the law. You're confusing party politics with legislation because the two are intertwined within the British constitution, but the Museum would be breaking the law and the entire directorate would be in a huge, huge amount of trouble if they just decided to ship the marbles off "on loan" any time soon without explicit changes in legislation.

[0] https://www.legislation.gov.uk/ukpga/1963/24

[swores]

If the museum were to argue that it is more in students' interest to see a poster explaining the importance of loaning something back to the country it came from (along with either a photo, or for anything where it's feasible even a real-looking replica), is there any chance they would actually get in trouble - beyond some negative op eds being written in the press?

Considering the law is a) interpreted by humans, and b) only something that matters if somebody both tries to enforce it and succeeds, I still feel they could do this despite what you point out. But I'm not at all an expert either on the subject of artifices like these or on the related legal issues, so you may well be right that it would cause them trouble if they followed my plan.

[PaulRobinson]

Yes, because the act says that isn't an acceptable disposal.

[swores]

I'm talking about calling it a loan, not officially getting rid of it. Who would take them to court to argue that it's actually a disposal rather than a loan?