The present invention is related to artificial lifting systems and production flow assurance from subsea oil wells. In this sense, the present invention provides an integrated subsea oil heating and pumping system hydraulically actuated by heated injection water, the system comprising at least one recoverable pumping module connected to a subsea base which, in turn, receives the produced fluids from at least one subsea producing well. The subsea base is connected to a production unit through a riser through which the produced oil flows and to an injection line that feeds the pumping module with water which, after activating the turbine and pump set, is injected through at least one injection well. The present invention further provides a hydraulically actuated subsea pumping method associated with the system described above.