You don't have to do anything. Its just an unique number for your application and in case in future you want to send some case specific enquiry or anything you have to mention your uci number.
I really hope that your prediction is true and I get some update. I have applied on 19th June and my medical isnt even passed yet and I am really worried. Cause medical gets update first.
I didnt call, i sent the case specific enquiry but no reply on that or anything. I got my answer on 24th august. Took 6 weeks. So you will have to wait!