The present invention relates to a cutting unit (1) for cutting labels (5) from a label film (6) in labelling machines, comprising a rotary blade drum (2) and a stationary blade assembly (3), the said stationary blade assembly (3) comprising a substantially U-shaped monolithic body (9) having a movable portion (10), a fixed portion (11) facing said movable portion (10) and linked thereto by a linking portion (12) and whereby to define a U-shaped groove therebetween, characterised in that the movable portion (10) of the monolithic body (9) comprises an adjustable support (19) for a blade (8), protruding from the end of the movable portion (10) that is proximal to the linking portion (12), a projecting element (19') defined by said adjustable support (19), the said blade (8) being connected to said projecting element (19').