The invention relates to a dispenser of rolls placed side by side, each held in rotation about a horizontal spindle (1), comprising a casing (10) surrounding the rolls, a cover (14) that complements the casing, at least one opening (2) in the lower part of the dispenser, and a sliding access panel (3) intended to partially close off the said opening so as to allow access to one of the rolls known as the roll in use, and at the same time, prevent access to the other roll known as the spare roll contained in the dispenser. According to the invention, the dispenser further comprises a mechanism intended to immobilize the access panel (3) under the spare roll and release it automatically and only when the roll in use is empty.