•A new method is presented for modelling the physical properties of galaxy clusters. •This technique moves away from the traditional approach of assuming specific parameterized functional forms for the variation of physical quantities within the cluster, and instead allows for a ‘free- form’ reconstruction, but one for which the level of complexity is determined automatically by the observational data. •Each cluster property is described as some interpolating function that is specified by a set of control points, or ‘nodes’, for which the number of nodes, together with their positions and amplitudes, are allowed to vary and are inferred in a Bayesian manner from the data. •This nodal approach is illustrated by modelling the electron pressure profile Pe(r) from Sunyaev–Zeldovich (SZ) observations of the cluster MACS J0744+3927 in the CLASH sample using Arcminute MicroKelvin Imager (AMI).