Withheld numbers won't show if the call comes via the 'direct' route - person A calls person B with the prefix 141 (or has previously arranged for all calls to default to 'Withheld') through the public network, and the default route ends with person B's exchange, or their mobile network. BT (and I assume KC and Virgin Media) accept the request to 'withhold' the number and it doesn't get passed on from the last exchange (but is available there, for logging purposes, such as for nuisance calls).
If person A calls a number which is provided by a service company (whether that number is geographic, or an 03xxx or 08, 09 {and possibly 070, and even to a mobile!}) then that company, routing the call to a recipient (such as myself, renting an 0800, or 03xxx, or 020, or 0131, etc), may offer person B the option of using CLI. I am sure it will depend on a company by company basis (the telecomm firms providing the numbers), and may be affected by their choice of equipment, plus their ingenuity/programming expertise (for the ability to allow individual customers to set/change options concerning incoming calls).
As I'm paying for incoming calls, eg for 0800 (and for the others too, even geographic numbers), then it seems fair to me that I know the number of the caller, and can decide whether I answer or not (esp if someone has been making nuisance calls to my business number). In the past, calls may have cost as much as 8p/min (and can still cost more than that if routed to a mobile, or abroad), so it was perhaps demanded by past customers.
Even ringing a
geographic (01/02) number may mean the call ends up the other side of the country and has CLI presented, if the number dialled was obtained via a service provider which gives the 'show CLI' option. It could equally end up (via VoIP) on a mobile, again with the number presented, whether the caller used 141 or not. Costs vary depending on the delivery method (where VoIP might be free, but obviously any 0800/0808/0500 call has some cost to the recipient, even if a really low cost method for delivery is used, and monthly fees may be charged on top, whether calls are made or not.
Edited by deleted (Sun 17-Nov-13 19:33:58)