Scene Designer is a novel method for searching and generating images using free-hand sketches of scene compositions; i.e. drawings that describe both the appearance and relative positions of objects. Our core contribution is a single unified model to learn both a cross-modal search embedding for matching sketched compositions to images, and an object embedding for layout synthesis. We show that a graph neural network (GNN) followed by Transformer under our novel contrastive learning setting is required to allow learning correlations between object type, appearance and arrangement, driving a mask generation module that synthesizes coherent scene layouts, whilst also delivering state of the art sketch based visual search of scenes.