Measuring the polarization of legislators and parties is a key step in understanding how politics develops over time. But in parliamentary systems—where ideological positions estimated from roll calls may not be informative—producing valid estimates is extremely challenging. We suggest a new measurement strategy that makes innovative use of the "accuracy" of machine classifiers, i.e., the number of correct predictions made as a proportion of all predictions. In our case, the “labels” are the party identifications of the members of parliament, predicted from their speeches along with some information on debate subjects. Intuitively, when the learner is able to discriminate members in the two main Westminster parties well, we claim we are in a period of “high” polarization. By contrast, when the classifier has low accuracy—and makes a relatively large number of mistakes in terms of allocating members to parties based on the data—we argue parliament is in an era of "low" polarization. This approach is fast and substantively valid, and we demonstrate its merits with simulations, and by comparing the estimates from 78 years of House of Commons speeches with qualitative and quantitative historical accounts of the same. As a headline finding, we note that contemporary British politics is approximately as polarized as it was in the mid-1960s—that is, in the middle of the "postwar consensus". More broadly, we show that the technical performance of supervised learning algorithms can be directly informative about substantive matters in social science.