You can set WordPress to approve or reject user registrations after admin review. WP Approve User is a free WordPress plugin that works in almost all WordPress versions. After activation it allows you to approve or unapprove user registrations and when you unapprove any user he gets blocked from access WordPress admin area dashboard.
Row action when user is approved:
Row action when user is not yet approved:
Error message when user is not yet approved:
Upon activation all existing users will automatically be flagged as approved and your blog admin will never experience restricted access and does not need approval.