The specific UK mechanism that is the subject of this subthread was introduced in July; it's not what your wikipedia link describes (social engineering to get a number ported).
I'm also in the UK, I've had the same phone number for at least a decade. It has been easy to carry your phone number to a new provider for as long as I can remember.
You just contact your existing provider, tell them you wish to leave and need the PAC code. After they beg to stay and throw you a sweetheart deal. They'll send it via text or post.
you have been ABLE to do that for as long as I can remember (I've kept the same number since 2005 now on all the major networks. I only didn't keep my number prior to that because it was a work provided contract) but depending on which you were dealing with would put up a number of different obstacles when you contact them to make the process as painful as possible (to keep you as a customer... THREE I'm looking at you!)
so the new automated SMS process introduced in July is a welcome addition
You just contact your existing provider, tell them you wish to leave and need the PAC code. After they beg to stay and throw you a sweetheart deal. They'll send it via text or post.