Depending on the contract they do. Often enough it's the GSM modem paging someone for alarms that holds a SIM with some old corporate contract that has no flatrate. And you'd violate the contract if you exchange it for some private contract SIM with all inclusive SMS.
Yes, every mobile phone operator in the UK charges for SMS and MMS if you're PAYG user. Users on contracts typically get 1000s of free SMS per month, but I'm not aware of any contracts that have inclusive MMS.