Unilamellar polymer vesicles are formed when a block copolymer self-assembles to form a single bilayer structure, with a hydrophobic core and hydrophilic surfaces, and the resulting membrane folds over and rearranges by connecting its edges to enclose a space. The physics of self-assembly tightly specifies the wall thickness of the resulting vesicle, but, both for polymer vesicles and phospholipids, no mechanism strongly selects for the overall size, so the size distribution of vesicles tends to be very polydisperse. We report a method for the production of controlled size distributions of micrometre-sized (that is, giant) vesicles combining the 'top-down' control of micrometre-sized features (vesicle diameter) by photolithography and dewetting with the 'bottom-up' control of nanometre-sized features (membrane thickness) by molecular self-assembly. It enables the spontaneous creation of unilamellar vesicles with a narrow size distribution that could find applications in drug and gene delivery, nano- and micro-reactors, substrates for macromolecular crystallography and model systems for studies of membrane function.