if you think PAF isnt involved in a war, your wrong. the war is all around us, everytime you step off base, your a target because the strike units are bombing the tribal belt on the afghan border.
2nd, you have to give up your citizenship completely, otherwise you arnt eligible at all. remember just giving up the passport wont do. you have to give up being British completely!
the other thing you need to consider is that when you do apply, be prepared to be interrogated, harassed and observed by the the intelligence guys. you will be treated like a spy. even after getting into the service. expect you lines to be tapped and a guy behind you. im not being paranoid. thats how things work here.
trust me, its just not worth the trouble