If you'd have instinctively swerved and hit a vehicle on your left, it would still be the fault of the driver who cut across your path. In the unlikely event that there were independent witnesses who could provide statements and the offending driver could be traced he (or his insurance company) would be liable to pay for the damage to your vehicle and to the one you hit. However, in reality he'd have just driven straight on and your insurance company would agree to treat the situation as if you were at fault. (However, you still couldn't be prosecuted for a motoring offence - or at least you shouldn't be!).
If you'd have not swerved (even though you had space to do so), the driver who cut across you would still be at fault. (Theoretically, lawyers could argue that you might be say, 5% or 10% to blame because you'd failed to exercise defensive driving techniques and anticipate his movement but, realistically, his insurance company would accept that he was to blame).
The driver of the police car might simply have been concentrating on his own driving, while his colleague (if any) was otherwise distracted. Alternatively, it could have just been the end of their shift and they wanted to avoid a load of paperwork ;-)
Chris