Using a mobile (texting or talking) has been banned in the UK for a few years now (hands-free is legal of course).
It's been a good thing as there have been too may idiots over here who've killed innocent people by losing control of their vehicle (e.g., trying to change gear with the wrong hand with none on the steering wheel).
Of course it still doesn't stop many from doing it and of the wayward driving I've seen, they've either been drunk or using a mobile. I think it's generally called driving 'without due care and attention' and the law that deals with that has been around for a while.
...and yes, the petition sounds a little over the top to me bearing in mind that the proposed legislation is meant to prevent potential serious injury or death at the expense of... well, not a lot really.
I think all pro's who drive, i.e., truck drivers, bus drivers, etc., and find it necessary to use a phone while driving have a hands-free device anyway because it's so much easier to use.