This study investigated lateral asymmetry in the linguopalatal speech sounds of British English by means of electropalatography. This instrumental technique visualizes tongue–palate contact during speech production and allows for the quantification of contact patterns. The first and main objective of the study was to establish a method of measuring asymmetry that would be more sensitive than the approach used previously and would facilitate statistical analysis. The method employed a modified index of asymmetry and controlled for the overall amount of tongue–palate contact. The secondary objective was to use the proposed method to quantify asymmetry in the production of the linguopalatal consonants of British English, focusing on asymmetry observed in the region of the palate corresponding to the place of articulation. Regression analysis of 22,004 speech sounds, produced by four native speakers, indicated that the approximant /l/ is the most asymmetrical speech sound, followed by the central approximants /j, r/. Although fricatives had been hypothesized to be highly asymmetrical, they were not consistently more asymmetrical than plosives. In terms of the place of articulation of speech sounds, velar sounds were less asymmetrical than alveolars. It was possible to account for some of these findings by referring to the unilateral productions of approximants.