I think I've solved the write permissions issue. My directory structure was \Volume_1\Backups and I was mounting \Volume_1\Backups. However, I hadn't set the write permissions properly on the Backups directory, so even though Volume_1 was writeable, Backups wasn't which is why I was being denied write access.
To set write permissions on Backups I went into My Files on the web admin interface, clicked on Volume_1, then in the right hand pane I right-clicked the Backups directory and selected Properties to edit the read/write permissions.
Thanks for everyone's help.