Travel / Travel to Poland without a Passport? I am British. [7]

I'm just wondering if its possible to cross over into Poland without a Passport.I've driven over many a times and never been stopped before but this time I'm on a coach going to Warsaw from Hannover.Due to some technicalities my British Passport still hasn't arrived which was sent for a renewal.I possess other forms of ID namely Drivers Licence etc.

My question is that is it worth taking the risk of being stranded on the border?