Most of the big nationals (aviation specific; RAFM, FAAM, Science Museum, National Museum of Flight etc) won’t receive loans unless it is something they specifically want for an exhibition and then between the parties the agreement is made out. The big nationals do talk to each other and almost all have items from each other’s collections within their own displays. There are so many examples of this. Most abide by the Museums Association and their codes of practise, so loan agreements are an easy process. As has been demonstrated here, a lot of smaller, less scrupulous museums are not bound by such things and do their own thng, which is where, if you are going to loan something to your local museum, make sure you protect yourself and your item, and get assurances behind its keeping within the museum, such as how it is stored or displayed and how secure the location is. If you are not happy with their criteria, walk away.