A dispenser and dispensing method for flexible web material that is wound into a roll on a readily deformable hollow core (C) has a housing carrying opposed parallel guide tracks (22-24) to guidingly receive roll core supports (E,F) projecting from the roll ends and a spring biased lever (40) pivoted on such housing, the lever (40) applying an axial force to the hollow core (C) at one roll end and being maintained in a roll retaining condition by the presence, in a roll dispensing position, of a hollow roll core that is held against downward displacement from such position. An axial force (FR) is applied against the other end of the hollow core. The lever (40) serves to retain a reserve roll (R) in a reserve roll position remote from the roll dispensing position with the lever (40) being released from such retaining condition when the web material is exhausted and the hollow core (C) is deformed downwardly, assisted by the axial forces (FR) applied to the hollow core ends, to enable removal of this core (C) from the roll dispensing position whereupon such reserve roll (R) moves to the dispensing position.