Compressive sensing is a lossy compression technique that is potentially very suitable for use in power constrained sensor nodes and Body Area Networks as the compression process has a low computational complexity. This paper investigates the reconstruction performance of compressive sensing when applied to EEG, ECG, EOG and EMG signals; establishing the performance of a signal agnostic compressive sensing strategy that could be used in a Body Area Network monitoring all of these. The results demonstrate that the EEG, ECG and EOG can all be reconstructed satisfactorily, although large inter- and intra- subject variations are present. EMG signals are not well reconstructed. Compressive sensing may therefore also find use as a novel method for the identification of EMG artefacts in other electro-physiological signals.