Future quantum based electronic systems will demand robust and highly accurate on-demand sources of current. Generating quantised current has immediate implications for quantum computing, quantum metrology, and electron interferometry. The ultimate limit of quantised current sources is a highly controllable device that manipulates individual electrons. We present a new single-electron pump mechanism, realised in a GaAs two-dimensional electron gas, where electrons are pumped through a one-dimensional split-gate confinement potential rather than more conventionally over a finger-gate potential. This new mechanism yields a new long pumping regime with quantised plateaus that are over two orders of magnitude longer than conventional pumps, and are extremely stable with respect to the applied voltages on the gates. The long plateaus are achieved via the combination of a saddle-point potential profile and enhanced quantum tunnelling, wherein the potential barrier height and shape are modified by the application of a source-drain bias. This new pumping regime cannot be explained by the simple geometrical electrostatic models or back-tunnelling theory that are used to describe conventional single-electron pumps, and we use a simple electrostatic model applied to split-gate confined pumps to explain some of the source-drain bias dependence.