The spin echo modulated small-angle neutron scattering technique has been implemented using two superconducting magnetic Wollaston prisms at a reactor neutron source. The density autocorrelation function measured for a test sample of colloidal silica in a suspension agrees with that obtained previously by other neutron scattering methods on an identically prepared sample. The reported apparatus has a number of advantages over competing technologies: it should allow larger length scales (up to several micrometres) to be probed; it has very small parasitic neutron scattering and attenuation; the magnetic fields within the device are highly uniform; and the neutron spin transport across the device boundaries is very efficient. To understand quantitatively the results of the reported experiment and to guide future instrument development, Monte Carlo simulations are presented, in which the evolution of the neutron polarization through the apparatus is based on magnetic field integrals obtained from finite-element simulations of the various magnetic components. The Monte Carlo simulations indicate that the polarization losses observed in the experiments are a result of instrumental artifacts that can be easily corrected in future experiments.