Storage units in Ashton. Storage space in Ashton-under-Lyne at Grosvenor Mill Business Centre which provides storage space in Ashton as well as storage to rent in Ashton. The storage space is for rent on flexible terms, using a simple licence agreement. Move in to your new Ashton storage space just by paying a deposit and a month's rent in advance, occupying the storage for a few months or a few years, walk in, sign up and move in to a new storage on the same day.