If the nut DieselDan mentioned isn't an 8mm allen one, then you'll need either a socket or crank wrench to get to it.
In the picture I attached, it looks to me like the "nut" is a lot bigger than 8mm. It is a little hard to see but it has a hex head and is the size you see in the picture. I will do your test to see if it is loose. I did wiggle it quite a bit and didn't see any play in it but i will try again.
Maybe it still is the pedal. I don't have a pedal wrench so it is hard to get it good and tight.