Thanks Wrathmonk and if it worked like that in practice then we would have oversight. If the police arrest first they gain additional powers to 'search without warrant'. Handily this avoids any requirement to see a judge or have any judicial oversight of what happens.
As I understand it the civilian police have to use search warrants more often as they usually do not have the evidence to proceed direct to arrest. As the grounds for arrest is so low in Service Law and is not subject to external scrutiny the RAFP can effectively bypass the judicial process by proceeding direct to arrest and then start the searches.