That version looks different from mine. Have you updated the app to the latest available on Google Play?
With the version I use, the "Unique ID" is not shown unless you gesture up on that QR code and it will then show.
If you are going to have someone scan your QR code to send a transaction to you, tap the QR code and it will show a larger version and your Unique ID will not show. Do not reveal your Unique ID to anyone. It is all that is needed to access the funds -- it is like a bearer instrument/bearer code.
That blockchain identifier is how you get access to be able to login to your Blockchain wallet. That link with the Blockchain identifier is what you might add to your bookmarks so that you can access the wallet at a later time, but it doesn't necessarily need to be kept secret.
You can edit your Blockchain account and associate an alias so that you don't even need to bookmark the URL with the identifier. You should also edit the account and add your e-mail address so that you can have it send you an encrypted backup of the wallet.
The Blockchain wallet requires a password to access the wallet, so that is the only thing you need to keep private.