An anchoring system for anchoring a tool (24) in a downhole tubular element (2) comprises: —an anchor (28) having a central body (40) connected to, or integrally formed with, the tool (24); —a slip element (50) radially movable relative to the central body (32) between a retracted and an expanded position against the inner surface of the tubular element (2), —a primary spring (56) for moving the slip element to the expanded position; —a control device comprising a stop member (60) against which the slip element (50) is pushed by the primary spring (56); and —a secondary spring (58) acting on the stop member (60) to move each slip element (50) to its retracted position.