It's your own fault for driving a BMW; everyone else automatically wants to screw over anyone driving one.
Seriously though, if I was ever clearly at fault for an accident I'd just cough to it. There's not a lot of point trying to scam your way out of it, you end up with three entities who all have your personal details (other party, their insurer, your insurer) all wishing you'd just stop being a selfish jackass and play fair.
You'll almost certainly lose at the end of it, and with these days of legal protection on policies (which I have too of course!) you'll then be hit for uninsured losses as well (NCB, excess, time spent disproving your bullshit).