Really depends on what locking system's on the door. On my metal up-and-over, the lock only secures the handle that you turn to open it. Once I've opened the door I can relock it and shut it from the inside. The handle then won't turn so it can't be opened from outside, but I can from the inside by pulling the cable that operates the catches.
You could add extra bolts by bolting them through the door with something like coach-bolts with round heads that can't be turned from the "wrong" side. In fact, I would, considering what you're keeping in there, and use good quality padlocks.
Don't forget to ask your landlord, I'm sure he wouldn't object to you adding extra security to his property.