A rotary positive displacement pump (1) that includes an impeller (3) that defines, within a pumping chamber (20), a plurality of successive chambers (21) with variable volume through which a fluid is mechanically conveyed from an inlet (7) to an outlet (8). The chambers (21) with variable volume are defined, at axially opposite ends, by a pair of rotational surfaces (40, 50) that close the pumping chamber (20) and are arranged to rotate about mutually inclined axes. Also described is a method of manufacturing the pump.