A laundry washing machine (100) has a washing tub (107) in which washing/rinsing liquid may be loaded; a rotatable perforated drum (110), in which laundry (112) to be washed can be loaded; a discharge system (145, 150) fluidly connected to the washing tub (107) and adapted to selectively discharge washing/rinsing liquid from the washing tub (107), the discharge system (145, 150) including a discharge duct (150) coupled with the washing tub (107) for receiving washing/rinsing liquid to be discharged; a pump (170) operable to selectively cause washing/rinsing liquid located in the discharge duct (150) to be discharged through a drain hose (175) or to be conveyed back into the washing tub (107) through a recirculation conduit (180). The pump (170) has: a) a pump chamber (230) for receiving washing/rinsing liquid from the discharge duct (150); b) a diverter element (240) movably arranged in the pump chamber (230) and movable between a first position, in which the diverter element (240) causes washing/rinsing liquid in the pump chamber (230) to be diverted to the recirculation conduit (180), and a second position, in which the diverter element (240) causes washing/rinsing liquid in the pump chamber (230) to be diverted to the drain hose (175).