I believe they do get that top level screening—Privy Council members as well.
Yes, it's going to reduce the number of people who could hold the position, but not so much that you're not going to have candidates for holding the Information Commissioner position. I think you want to have someone with that type of security screening for lots of other things that they would be reviewing as well, not just national security measures, and it's knowing that this person is going to take the role seriously and look at it.