Radio interferometers used to make astronomical observations, such as the LOw Frequency ARray (LOFAR), experience distortions imposed upon the received signal due to the ionosphere as well as those from instrumental errors. Calibration using a well-characterised radio source can be used to mitigate these effects and produce more accurate images of astronomical sources, and the calibration process provides measurements of ionospheric conditions over a wide range of length scales. The basic ionospheric measurement this provides is differential Total Electron Content (TEC, the integral of electron density along the line of sight). Differential TEC measurements made using LOFAR have a precision of <1 mTECu and therefore enable investigation of ionospheric disturbances which may be undetectable to many other methods. We demonstrate an approach to identify ionospheric waves from these data using a wavelet transform and a simple plane wave model. The noise spectra are robustly characterised to provide uncertainty estimates for the fitted parameters. An example is shown in which this method identifies a wave with an amplitude an order of magnitude below those reported using GNSS TEC measurements. Artificially generated data are used to test the accuracy of the method and establish the range of wavelengths which can be detected using this method with LOFAR data. This technique will enable the use of a large and mostly unexplored dataset to study travelling ionospheric disturbances over Europe.