Antonyms for the phrase "allowing use of" could include prohibiting, preventing, disallowing, forbidding, and denying. These words all suggest a refusal or limitation on the use of something, whether it be a physical object like a space or a tool, or an abstract concept like an idea or a right. In contrast to "allowing use of," these antonyms suggest a more restrictive or controlling approach to granting access or permission. While there may be situations where these words are appropriate, in general, it is more productive to seek ways to allow for greater access and collaboration, instead of imposing unnecessary limits.