No he cannot restrict you. This is because you are entitled to the whole house including the basement. You are supposed to know what is in that room and have the access to it. If something could happen and the authority come to your house, they would count everything as your property including what is in the basement.
It's undoubtedly locked for security, but you should have a key. Normally the rent you pay entitles you to access to your storage unit as well as your apartment. You should read your lease to see if you agreed to some other setup.