An integrated modelling methodology for the calculation of realistic plasma neutron sources for the JET tokamak has been developed. The computational chain comprises TRANSP plasma transport and DRESS neutron spectrum calculations, and their coupling to the MCNP neutron transport code, bridging plasma physics and neutronics. In the paper we apply the developed methodology to the analysis of neutron emission properties of deuterium and helium plasmas at JET, and validate individual modelling steps against neutron diagnostic measurements. Two types of JET discharges are modelled-baseline-like and three-ion radio-frequency scenarios-due to their diversity in plasma heating, characteristics of the induced fast ion population, and the imprint of these on neutron emission properties. The neutron emission modelling results are quantitatively compared to the total neutron yield from fission chambers, neutron emissivity profiles from the neutron camera, neutron spectra from the time-of-flight spectrometer, and neutron activation measurements. The agreement between measured and calculated quantities is found to be satisfactory for all four diagnostic systems within the estimated experimental and computational uncertainties. Additionally, the effect of neutrons not originating from the dominating D(D, n)He-3 reactions is studied through modelling of triton burnup DT neutrons, and, in mixed D-He-3 plasmas, neutrons produced in the Be-9(D, n gamma)B-10 reaction on impurities. It is found that these reactions can contribute up to several percent to the total neutron yield and dominate the neutron activation of samples. The effect of MeV-range fast ions on the neutron activation of In-115 and Al-27 samples is measured and computationally validated.