Re: It probably doesn't bother cops that much.
The cops have to get into your phone to get at these plain text logs though. They have to make you unlock it first, which at minimum will require a warrant. Even then, could they force you to unlock it with your fingerprint in the UK? I know they can force you to give up your password over there, but that's not the same thing.
If they could do so, and you were really paranoid, it would be nice if Apple had a coercion erasure feature, so you could program a different finger you'd use to unlock the phone triggering an instant, silent erasure. "Sorry officer, I just had my phone replaced earlier today and haven't had time to restore it from backup yet"
If you trigger the erasure accidentally, well, let's just say that's incentive to backup often!