We use data from the Herschel-ATLAS to investigate the evolution of the far-infrared-radio correlation over the redshift range 0 < z < 0.5. Using the total far-infrared luminosity of all >5σ sources in the Herschel-ATLAS Science Demonstration Field and cross-matching these data with radio data from the Faint Images of the Radio Sky at Twenty-Centimetres (FIRST) survey and the NRAO Very Large Array (VLA) Northern Sky Survey (NVSS), we obtain 104 radio counterparts to the Herschel sources. With these data we find no evidence for evolution in the far-infrared-radio correlation over the redshift range 0 < z < 0.5, where the median value for the ratio between far-infrared and radio luminosity, qIR, over this range is qIR = 2.40 +/- 0.12 (and a mean of qIR = 2.52 +/- 0.03 accounting for the lower limits), consistent with both the local value determined from IRAS and values derived from surveys targeting the high-redshift Universe. By comparing the radio fluxes of our sample measured from both FIRST and NVSS we show that previous results suggesting an increase in the value of qIR from high to low redshift may be the result of resolving out extended emission of the low-redshift sources with relatively high-resolution interferometric data, although contamination from active galactic nuclei could still play a significant role. We also find tentative evidence that the longer wavelength cooler dust is heated by an evolved stellar population which does not trace the star formation rate as closely as the shorter wavelength <~ 250μm emission or the radio emission, supporting suggestions based on detailed models of individual galaxies. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. E-mail: m.j.jarvis [at] herts.ac.uk (m[dot]j[dot]jarvis[at]herts[dot]ac[dot]uk)