CIC call centre agents generally will not entertain queries regarding status of UCI number.
You need a bit of luck here. Having said this, I got my UCI number twice, (the second time, I checked just to cross check if the number was correct). Mary, Mark and Elizabeth are 3 agents whom I found helpful. So if they answer your call, you might be lucky.
Also, you will have to be more tactful. You will need to convince them why the UCI is so important to you. If the agent is not cooperative, he will never help, no matter how much you try. So just disconnect if you feel the agent is not budging and then try again to get connected to some more helpful agent.
Hope this helps.