We investigated the boundary conditions for flow of a Newtonian liquid over soft interfaces by measuring hydrodynamic drainage forces with colloid probe atomic force microscopy in a viscous liquid. The investigated soft surfaces are end-grafted brushes of thiolated poly(ethylene glycol) (PEG), of molecular weight 1k and 30k, grafted-to gold. The conditions for brush preparation were optimized as to meet the stringent conditions required for surface force measurements, namely reproducible and uniform surface composition and roughness. The fit of a slip model to the experimental data returned a slip length of 16 nm on the PEG 1k brush and 25 nm on the PEG30k brush. The slip length can be interpreted as a penetration length, which accounts for flow within the top half of the brush for the PEG30k case, and within the brush and surface roughness for the PEG1k case. These findings confirm earlier simulation studies by our group on the flow of liquids within polymer brushes.