JAA flight schools write their own training manual which has in it the limits.
Like Whirlygig said itīs very usual to have 8km & 2000' . Often there are wind limts as well, such as 15 kts for solo students for example!
I would think that only the chief instructor / Head of training or flight operations manager could give permission to fly in the weather worse than the limits in the handbook allow and then only for a good reason.