A high-pressure fuel supply pump for a fuel system that supplies a high-pressure fuel injection (GDI) apparatus and a low-pressure fuel injection (PFI) apparatus incorporates an inlet check valve to isolate a low-pressure fuel feed channel in the pump from pressure fluctuations at the inlet of an inlet control valve. Upstream of the inlet check valve, the low-pressure fuel feed channel is connected to a seal chamber surrounding the pumping plunger. Circulating fresh low-pressure fuel through the seal chamber ensures that the pumping plunger and the clearance between the plunger and the pump bore are cooled and lubricated with fuel, even when high pressure fuel is not produced by the high-pressure pump. The low-pressure fuel feed channel is connected to the low-pressure PFI outlet downstream of the seal chamber. This pump configuration provides stable source of low-pressure fuel for a PFI system.