If your BMW is written off...
...the payout from your motor insurer could well be less than the amount outstanding on finance at the time of claim. If it is, you'd have to pay any shortfall out of your own pocket before you could even think about financing a new vehicle.
...the finance house will calculate a settlement figure which is normally a combination of what they believe the vehicle to have been worth at the time of loss plus the sum of rentals that you've not yet paid for the remaining duration of the lease. Your motor insurer's payout could well be less than the amount of this settlement figure and although some houses allow you to walk away from any shortfall, others require you to pay some of it and others still might well require you to pay all of the shortfall.
Just like with a financed vehicle, if you're liable for any shortfall, you'd have to fund that out of your own pocket before you could even think about leasing another vehicle.
...your motor insurance payout is almost certainly going to be less than the price you bought your vehicle for originally (afterall almost all vehicles depreciate in value over time). Without GAP insurance in place, you'll only have the amount paid out by your Motor Insurer with which to replace your vehicle. If you want to buy a more expensive vehicle, you'll have to fund the difference out of your own pocket.
It's a popular misconception that GAP insurance isn't required to cover a BMW that you paid cash for. However we believe that it's more important for a cash-buyer to have GAP insurance in place than perhaps any other.