The simple membership plugin has a feature that allows you to manually approve your members.
Step 1) Go to the settings menu of the membership plugin.
Step 2) Select “pending” as the “Default Account Status” field’s value.
Now, all the members that signup will have an account status of “pending” so they can’t log into the site.
You (the site admin) can go to the members menu and review the pending account(s) and set it to “active”.
Step 3) Go to the “Email Settings” menu and edit the content of the “Registration Complete” email so it says something along the lines of:
Your account is under review. You will be able to log into the site after an admin approves your account.
Step 4) Optionally, you can send a notification email to the members letting them know that their account has been approved. Read the sending a quick notification email documentation to learn how to do this.
Email Activation Feature
Simple Membership plugin also has an email activation feature that may be useful for you. Check out how the email activation feature works.