The influence of the physicochemical conditions on permeation rate in cross-flow ultrafiltration of colloidal suspension is investigated. A model is developed using simple hydrodynamics for the flow in a rectangular channel with one porous wall, but focusing on a detailed description of the dependence of both osmotic pressure and gradient diffusion coefficient on concentration and physicochemical parameters. The analysis is based on a fundamental calculation of colloidal interactions between particles expressed in terms of osmotic pressure. The osmotic pressure modelling accounts for multiparticle electrostatic interactions, dispersion forces and configurational entropy effects. The osmotic pressure is further used in the calculation of the gradient diffusion coefficient from the generalized Stokes-Einstein equation. The cross-flow ultrafiltration model yields an a priori prediction (with no adjustable parameters) for the filtration rate of colloids at various operating conditions (applied pressure, cross-flow rate, membrane resistance) as a function of particle size, zeta potential or surface charge, and ionic strength. Model predictions are compared to experimental filtration data for the protein bovine serum albumin (BSA).