PhonePay Plus publishes an information leaflet which strongly suggests the answer to the hanging question -
http://www.phonepayplus.org.uk/upload/PhonepayPlus_Shortcodes_and_text_subscript....
Shortcode texts commonly incur a service fee, in addition to the basic charge for any text message levied by your service provider, and the level of that fee must be advised. This split cost basis is very different from that which currently applies to voice telephone calls where a single rate applies to each particular combination of service and provider.
You would probably pay to send a "STOP" notice. If you have not subscribed to a subscription service, then this should not be necessary to avoid unwanted costs, as you cannot be (properly) charged for services to which you have not subscribed. Requiring a "STOP" notice to prevent unwanted (non-chargeable) information is, in my view, an abuse of the principles.
Unsolicited marketing messages by SMS are prohibited under the PECR regulations enforced by the ICO. SMS falls within the definition of "email" in this context. As there is a general prohibition, the TPS is irrelevant. Those to whom one has provided a mobile number in the course of doing business are entitled to send further relevant information by SMS. They must however offer a clear opportunity to decline such information and repsect such a request. As I understand the specific regulations, they are entitled to use a chargeable service for one to make contact with them. I cannot however believe that they could refuse to respond to communications by other means, from which they do not derive income, demanding that they stop sending unwanted text messages. I am sure that the ICO would be able to clarify this.
The precise terms of any mobile service (i.e. the basic cost of sending SMS) should be declared by the mobile service provider. The level of any additional charge (note the difference between this and telephone calls) must be declared by the provider of that additional service.
(I hope this is accurate and helpful.)