In fact, there is a workaround, but you must sacrifice another feature of Clipboard. If you turn off in the Alfred's Clipboard settings that you do not want to "Keep File Lists", as per the screenshot below, then the issue resolves itself. This is something, which has been getting on my nerves for a very long time.
This is the tip I got from Alfred support, and it did in fact work. Since, I predominantly use clipboard history for text and images, I don't mind not having the file lists in the clipboard history.