The large astrometric and photometric survey performed by the Gaia mission allows for a panoptic view of the Galactic disc and in its stellar cluster population. Hundreds of clusters were only discovered after the latest Gaia data release (DR2) and have yet to be characterised. Here we make use of the deep and homogeneous Gaia photometry down to G=18 to estimate the distance, age, and interstellar reddening for about 2000 clusters identified with Gaia DR2 astrometry. We use these objects to study the structure and evolution of the Galactic disc. We rely on a set of objects with well-determined parameters in the literature to train an artificial neural network to estimate parameters from the Gaia photometry of cluster members and their mean parallax. We obtain reliable parameters for 1867 clusters. Our new homogeneous catalogue confirms the relative lack of old clusters in the inner disc (with a few notable exceptions). We also quantify and discuss the variation of scale height with cluster age, and detect the Galactic warp in the distribution of old clusters. This work results in a large and homogenous cluster catalogue. However, the present sample is still unable to trace the Outer spiral arm of the Milky Way, which indicates that the outer disc cluster census might still be incomplete.