We report the discovery of 16 detached M dwarf eclipsing binaries with J < 16 mag and provide a detailed characterization of three of them, using high-precision infrared light curves from the WFCAM Transit Survey (WTS). Such systems provide the most accurate and model-independent method for measuring the fundamental parameters of these poorly understood yet numerous stars, which currently lack sufficient observations to precisely calibrate stellar evolution models. We fully solve for the masses and radii of three of the systems, finding orbital periods in the range 1.5 < P < 4.9 d, with masses spanning 0.35–0.50 M⊙ and radii between 0.38 and 0.50 R⊙, with uncertainties of ∼3.5–6.4 per cent in mass and ∼2.7–5.5 per cent in radius. Close companions in short-period binaries are expected to be tidally locked into fast rotational velocities, resulting in high levels of magnetic activity. This is predicted to inflate their radii by inhibiting convective flow and increasing starspot coverage. The radii of the WTS systems are inflated above model predictions by ∼3–12 per cent, in agreement with the observed trend, despite an expected lower systematic contribution from starspot signals at infrared wavelengths. We searched for correlation between the orbital period and radius inflation by combining our results with all existing M dwarf radius measurements of comparable precision, but we found no statistically significant evidence for a decrease in radius inflation for longer period, less active systems. Radius inflation continues to exists in non-synchronized systems, indicating that the problem remains even for very low activity M dwarfs. Resolving this issue is vital not only for understanding the most populous stars in the Universe, but also for characterizing their planetary companions, which hold the best prospects for finding Earth-like planets in the traditional habitable zone.