A method for rewinding a web of sheet material for making a log wound on a core in a winding zone formed between an upper winding roller and a lower winding roller. Upstream of the winding zone a cradle is provided for feeding the core connected to the support of the lower roller and located beneath the upper winding roller. At least a portion of the cradle is movable with respect to the support of the lower roller and is capable of lowering or rising towards/away from the upper winding roller. For each step of feeding a core, the movable portion can be displaced from a first position of load of the core to a second position wherein the core contacts the upper roller. When the upper roller contacts the core for reaching the winding zone it moves first on the movable portion and then on a fixed portion of the cradle that is integral to the support wherein the axle rotates of the lower roller.