We describe the fabrication and characterisation of a capacitive pressure sensor formed by an ultra-thin graphene-polymer heterostructure membrane spanning a large array of micro-cavities each up to 30 μm in diameter with 100% yield. Sensors covering an area of just 1 mm2 show reproducible pressure transduction under static and dynamic loading up to pressures of 250 kPa. The measured capacitance change in response to pressure is in good agreement with calculations. Further, we demonstrate high-sensitivity pressure sensors by applying a novel strained membrane transfer and optimising the sensor architecture. This method enables suspended structures with less than 50 nm of air dielectric gap, giving a pressure sensitivity of 123 aF Pa-1 mm-2 over a pressure range of 0 to 100 kPa.