Hi @HorribleHarry, thanks for messaging the Community!
If you're able to access your music files in the iOS Files app, then you might be able to upload them to the Dropbox mobile app onto your account.
Generally, the Music app on iOS prevents any kind of transfer to a third party service for copyright purposes. Files can only be synced directly to and from iTunes on the desktop.
If you have any further queries, feel free to message back.