A new method is presented for modelling the physical properties of galaxy clusters. Our 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 'freeform' reconstruction, but one for which the level of complexity is determined automatically by the observational data and may depend on position within the cluster. This is achieved by representing each independent cluster property as some interpolating or approximating 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. We illustrate our nodal approach in the case of a spherical cluster by modelling the electron pressure profile P e (r) in analyses both of simulated Sunyaev-Zel'dovich (SZ) data from the Arcminute MicroKelvin Imager (AMI) and of real AMI observations of the cluster MACS J0744+3927 in the CLASH sample. We demonstrate that one may indeed determine the complexity supported by the data in the reconstructed P e (r), and that one may constrain two very important quantities in such an analysis: the cluster total volume integrated Comptonization parameter (Y tot ) and the extent of the gas distribution in the cluster (r max ). The approach is also well-suited to detecting clusters in blind SZ surveys, in the case where the population of radio sources is known in advance.