RXJ1720.1+2638 is a cool-core, ‘relaxed-appearing’ cluster with a minihalo previously detected up to 8.4 GHz, confined by X-ray-detected cold fronts. We present observations of the minihalo at 13–18 GHz with the Arcminute Microkelvin Imager telescope, simultaneously modelling the Sunyaev–Zel’dovich signal of the cluster in conjunction with Planck and Chandra data in order to disentangle the non-thermal emission of the minihalo. We show that the previously reported steepening of the minihalo emission at 8.4 GHz is not supported by the AMI data and that the spectrum is consistent with a single power law up to 18 GHz. We also show the presence of a larger scale component of the minihalo extending beyond the cold fronts. Both of these observations could be explained by the ‘hadronic’ or ‘secondary’ mechanism for the production of relativistic electrons, rather than the currently favoured ‘re-acceleration’ mechanism and/or multiple episodes of jet activity from the active galactic nucleus in the brightest cluster galaxy.