Boson sampling is an example of a non-universal quantum computation which is believed to be feasible in the near term and cannot be simulated on a classical machine. Like all purported demonstrations of "quantum computational supremacy", this motivates optimizing classical simulation schemes for a realistic model of the problem, in this case including lost or distinguishable photons. Although current schemes for sufficiently imperfect boson sampling are classically efficient, the polynomial runtime can be infeasibly large. Using a novel first quantized approach, we develop a scheme for classical simulation of boson sampling under uniform distinguishability and loss, based on sampling from distributions where at most k photons are indistinguishable. We show that asymptotically this scheme can provide a polynomial improvement in the runtime compared to classically simulating the idealised case. More significantly, we show that in the regime currently considered experimentally relevant, our approach gives a substantial improvement over the best known classical approaches. We conclude with some interesting observations regarding the complexity of simulating noisy versions of supremacy experiments.