The identification of corrosion, cracks and defects in pipelines used for transporting oil and gas can reduce the possibility of leaks, and consequently, it can limit the extent of an environmental disaster, public hazard and the associated financial impact of such events. Typically, corrosion in oil pipelines is measured with non-destructive ultrasonic or electromagnetic techniques, on the basis that corrosion and defects are often manifest as a change of thickness in the steel from which pipelines are made. However, such approaches are not practical for underground pipelines and their deployment can be complicated for the case of pipelines covered by insulation. In this paper, we present an innovative, non-destructive testing technique, which exploits the backscatter of a combination of fast-neutron and γ radiation from steel samples of a variety of thicknesses consistent with changes that might arise due to corrosion of a pipe wall. Our research demonstrates the potential to measure and characterise different steel thicknesses by detecting both the elastic, fast-neutron backscatter and the Compton-scattered γ radiations, simultaneously. Further, we demonstrate that the presence of insulation yields a consistent and separable influence on the experimental, wall-thickness measurements. The data from experimental measurements are supported by a comprehensive Monte Carlo computer simulation study.