First, realize that it's not limited liability by itself that insulates companies from the costs of their activity. Even without limited liability, it's just not really illegal to pollute. If your pollution increases my risk of lung cancer by 250%, that is something that has a cost. You can put a dollar value on that statistical probability. But you can't sue over it, because by and large outside of medical malpractice it's nearly impossible to sue for statistical injuries.
Second, individual private suits will never internalize even a fraction of the cost of an externality. When you're sitting in a lab with a computer simulation, you can look at the data and do a good estimate of how many cases of lung cancer can be attributed to the nearby coal plant, but it's nearly impossible to meet the necessary burden of proof with regard to one particular case. Say one factory causes 10% of all the lung cancer cases in one part of the city. The burden of proof in civil litigation is more likely than not. For any given case of lung cancer, it is not more likely than not that the factory was the cause. We don't allow suits based on statistically divisible causality.
Third, enough people won't sue. Partly because most people will have no idea what caused their injuries, but also because a disproportionate number of people injured by pollution are poor. They're ignorant of the legal system and don't have money for lawyers. Lawyers won't take such cases on contingency, because winning is nearly impossible.
Fourth, even when the suits are successful, defendants will pay a fraction of what they should, because they'll pay a team of $1,000/hour lawyers to make sure they do. BP is probably paying Kirkland & Ellis $1,000/minute, and its worth every penny because they're saving billions of dollars.
A smart man once pointed out: "When large numbers of people are involved, the argument for the institution of property rights is weakened and that for general regulations becomes stronger." Ronald Coase, "The Federal Communications Commission," 2 J. Law and Economics 1, 29 (discussing spectrum allocation, but using smoke pollution as an example). Coase is of course one of the luminaries of modern economics, and his theories are the bedrock of conservative political policies.