Check again....
http://www.productsandservices.bt.com/consumerProduc...
"BT Privacy with Caller Display will cost £1.75 a month from 4 January 2014, but existing customers of the service can pre-register to continue getting it free for 12 months°. Find out more and register at bt.com/freecallerdisplay. BT Privacy with Caller Display will remain free for BT Basic customers."
Then click on "The legal stuff"
"BT Privacy with Caller Display Free for 12 months � Pre-register before 6th December 2013 at bt.com/freecallerdisplay. Pre-registration available only to existing BT Privacy with Caller Display customers � excludes customers with other varieties of Caller Display (such as Caller Display as part of a Calling Features Pack). Provides BT Privacy with Caller Display free for 12 months from date of provision. A new 12-month Line Rental contract applies. Visit bt.com/freecallerdisplay for more information."
Key part here is "A new 12-month Line Rental contract applies"
http://home.bt.com/news/btlife/get-bt-privacy-with-c...
Choice is a NEW 12 MONTH contract with BT to get free caller ID, or pay £1.75/month
Also check back to your BT calling package page post price change and you will find it has a price against it. 1571 shows free at the moment, it will change to show as a charged for service come Jan 4th.