no offence dude but Sports mode on and DSC off on a public road with 340 bhp on the rear wheels and a new vehicle for you= what were you thinking?

You are a good sport in understanding and stating where you went wrong
We all "push" our cars at some point but the limits on the M are high so you can quickly end up in some serious trouble.
Its quite a short wheel base and whilst the car's suspension set up does mean understeer and is progressive, I frankly even after plenty of track time would not be cocky enough to say that I can drive it on the road "on the limit". It take a fair bit of practice to control a slide. Attempts normally and up in "saugaging" the car as the back end move rapidly sideways you countersteer and let go of the trottle at the same time.
Take some track time with an instructor, its well worth it and you'll learn to get closer to the limit safely.
The fact that the chassis is pretty good and the engine is so, powerfull does hinder progress somewhat to be fair, its not the easyest of cars to learn in colpared to say a Caterham.