BT 4600 phone - caller I’d not working

[Isabelh2]

Hi I have just purchased a BT 4600 telephone and caller I’d does not work. I currently have it plugged in to the phone socket on the wall. However I am thinking I need a new router so I can plug it in to that. Is this correct and how do I get a new router?  Current router is a few years old and does not have a port for phone connection. 
any help would be much appreciated. 

[XRaySpeX]

Do you have any other landline phones at home? Do they show CLI?

Have you been converted to Digital Voice (DV) landline? If so, you should have been sent a suitable EE router & you plug your phone into the back of that.

Which EE router & WiFi extenders, if any, do you have (read label or post a pix)? What is the name of the EE BB plan you are on including its speed?

What does BT Wholesale Broadband Availability Checker > Address Checker estimate for your address? Post the whole table, the text below it and the line above it, blanking out your address.