The rheological properties of plastic and viscoplastic complex fluids have been investigated using constant velocity squeeze flow rheometry at small gaps in order to examine the influence of the resulting flow confinement. The fluids investigated were aqueous carbopol suspensions and three commercial products (Tesco English mustard, Tesco value lemon curd and Heinz tomato ketchup (HTK)). The bulk rheological properties were measured using parallel plate rheometry. Rough plates were used to eliminate wall slip in both rheometric configurations. The commercial products are Herschel–Bulkley fluids and, for gaps less than a critical value of ~200 μm, the yield stresses tended to large values. There was a corresponding trend to small values for the flow consistencies except for HTK, which has a negligibly small bulk value. A possible explanation is that the micro-structural correlation lengths of these fluids are of the order of that of the critical separation. The yield stresses of the carbopol suspensions also increased sharply at the critical gap but then decreased gradually with decreasing gap separation. The transition may correspond to the formation of a jammed state with the subsequent plastic flow at smaller gap separations arising from localised shearing.