Yes, £1.75 per month iirc. You don't pay for it on mobile phones, because the operators choose not to charge you for it. Actually, I think its more to do with it being a part of the digital GSM (2G) specification whereas CD on landlines was always an optional technology.
There are some providers (Sky Talk for instance) who provide CD at no extra cost.
Quite why anyone is still with BT though, is beyond me, shite pricing, shite services, shite support, a company with zero morals, and nobody honestly has any reason to stay with them.
They are such scum, they added it to my account randomly one bill without even asking me (amongst other things they were incorrectly billing me for). Then I had murder (and a lot of wasted time) trying to get them to remove it, 30 minutes on the phone to be told by an Indian that he could not understand what I was saying, takes the pi$$). I only use my landline for DSL and 08 calls, so why the hell would I need CD the morons. When you have a mobile with unlimited calls, web and texts, and your not at home very often, you don't tend to need to use a shitty overpriced landline.
Never had any such trouble with Madasafish or Sky Talk, and the former are considerably cheaper than most other providers, including BT (though the owners of Madasafish are a subsidury of the BT Group, it seems, fortunately, that is where the similarities with BT Retail end).