can orange block my phone or just my sim card?….?

I am having a dispute with orange where they have taken my bill off me twice & are fefusing to accept responsibility or refund me. I also have my mobile phone with orange. Basically I need to know if I cancel my mobile phone & broadband contracts with immediate effect, due to the way that they have treated me, can orange block my phone if i use it with a different PAYG sim card? or would they just block the sim card? thanks