Unfortunately, the web interface does not provide a way to move files.
If you need to do this from a Mac, you could try using the u1ftp API demonstration program I wrote, which lets you manage your files through a stub FTP server running locally.
Simply download the ZIP file from https://launchpad.net/u1ftp and run the following from the terminal:
Now use an FTP client to connect to
localhost on port
2121 using your Ubuntu One credentials. Performing moves or renames should happen fully server side, and avoid re-uploading the files.
While MacOS's Finder has some FTP capabilities, it only supports read-only operations so is not suitable for this job. Pretty much any of the dedicated FTP clients should do the trick though.