In this paper, we present a novel computational approach to the analysis of accent variation. The case study is dialect levelling in the North of England, manifested as reduction of accent variation across the North and emergence of General Northern English (GNE), a pan-regional standard accent associated with middle-class speakers. We investigated this instance of dialect levelling using random forest classification, with audio data from a crowd-sourced corpus of 105 urban, mostly highly-educated speakers from five northern UK cities: Leeds, Liverpool, Manchester, Newcastle upon Tyne and Sheffield. We trained random forest models to identify individual northern cities from a sample of other northern accents, based on first two formant measurements of full vowel systems. We tested the models using unseen data. We relied on undersampling, bagging (bootstrap aggregation) and leave-one-out cross-validation to address some challenges associated with the data set, such as unbalanced data and relatively small sample size. The accuracy of classification provides us with a measure of relative similarity between different pairs of cities, while calculating conditional feature importance allows us to identify which input features (which vowels and which formants) have the largest influence in the prediction. We do find a considerable degree of levelling, especially between Manchester, Leeds and Sheffield, although some differences persist. The features that contribute to these differences most systematically are typically not the ones discussed in previous dialect descriptions. We propose that the most systematic regional features are also not salient, and as such, they serve as sociolinguistic regional indicators. We supplement the random forest results with a more traditional variationist description of by-city vowel systems, and we use both sources of evidence to inform a description of the vowels of General Northern English.