M dwarfs are prime targets in the hunt for habitable worlds around other stars. This is due to their abundance as well as their small radii and low masses and tempera- tures, which facilitate the detection of temperate, rocky planets in orbit around them. However, the fundamental properties of M dwarfs are difficult to constrain, often lim- iting our ability to characterise the planets they host. Here we test several theoretical relationships for M dwarfs by measuring 23 high precision, model-independent masses and radii for M dwarfs in binaries with white dwarfs. We find a large scatter in the radii of these low-mass stars, with 25 per cent having radii consistent with theoret- ical models while the rest are up to 12 per cent over-inflated. This scatter is seen in both partially- and fully-convective M dwarfs. No clear trend is seen between the over-inflation and age or metallicity, but there are indications that the radii of slowly rotating M dwarfs are more consistent with predictions, albeit with a similar amount of scatter in the measurements compared to more rapidly rotating M dwarfs. The sample of M dwarfs in close binaries with white dwarfs appears indistinguishable from other M dwarf samples, implying that common envelope evolution has a negligible impact on their structure. We conclude that theoretical and empirical mass-radius relationships lack the precision and accuracy required to measure the fundamental parameters of M dwarfs well enough to determine the internal structure and bulk composition of the planets they host. Peer Reviewed