Karl, I bought my phone outright, unlocked, and GiffGaff is my service provider at the moment.
From the GiffGaff page:
"If you selected to block your phone, it will be put on a national blacklist and no-one will be able to use it.
Even once your phone has been blocked, we advise to change the password for the different applications you may have been running on your phone (email, instant messaging, ...).
f you need to unbar your phone you can do it by contacting an agent here and providing us with your IMEI number. You can find your IMEI number by dialling *#06# with your phone, or on the phone's original box. It will take around 5 working days to unbar your phone."
Every mobile phone service provider can block your phone and SIM card.