Couldn't you just turn your phone off for the duration of the exam and keep it in your pockets? That way, if you do have your phone in your bag, you don't have to panic if someone goes through your bag provided what shinny said above was correct.
Surely they wouldn't go through your pockets to see if you have a phone on you...
They wouldn't, but they might see the outline or something. Even so, in uni exams, before I went to the toilet, they had me pat my pockets first to show I didn't have a phone on me, and it's particularly for this reason that even a turned-off phone isn't allowed whatsoever on you. Whilst obviously it's not smart just putting your phone on the floor, I doubt anyone's going to steal an entire bag though, so just bring a bag along and chuck your stuff in there.
For Monash exams at Caulfield Racecourse, when my friend and I used the toilets inside the venue before the exams started... we were asked to leave our bags outside the bathroom.
They probably figured we could take out notes, put them somewhere, then come check them during the exam during a 'toilet break' or something.
Yet, if someone really wanted to do this... they could simply keep said notes on their person (and either put them somewhere in the bathroom, or keep them in their pocket).
Also... for Monash exams... anything on the floor under your desk does not count as being on your person.
Obviously you can't have visible notes or something at your feet, but we don't have to put our bags at the front of the room like you guys do... we put them at our feet.
I've also never had an examiner tell me off for having food (think skittles), my glasses, my glasses case, or my mini-clock on the desk (none of which, strictly speaking, are permitted).
I've only ever been asked to open my glasses case to show there was nothing concealed in there.
Oh, and an invigilator has once asked me to look directly at her during the exam so that she could check that the face on my ID card was indeed mine.
I don't blame her for that one tho... the ID card printer thingy threw a spasm when it printed mine... it printed my face in interesting hues of blue XD
Anywayz... if you *just* want to take your wallet... I'd take a jacket with you, put the wallet in your jacket pocket, and sit the jacket over your chair.
Don't take your phone with you if you don't intend to take a bag, because then you'll have troubling keeping it safe during the exam.
If you really think you'll need to make a call, make sure you've got a couple of coins in your wallet so you can use a pay phone.