The EDGE2D-EIRENE code is applied for simulation of divertor detachment during matched density ramp experiments in high triangularity, L-mode plasmas in both JET-Carbon (JET-C) and JET-ITER-Like Wall (JET-ILW). The code runs without drifts and includes either C or Be as impurity, but not W, assuming that the W targets have been coated with Be via main chamber migration. The simulations reproduce reasonably well the observed particle flux detachment as density is raised in both JET-C and JET-ILW experiments and can better match the experimental in-out divertor target power asymmetry if the heat flux entering the outer divertor is artificially set at around 2–3 times that entering the inner divertor. A careful comparison between different sets of atomic physics processes used in EIRENE shows that the detachment modelled by EDGE2D-EIRENE relies only on an increase of the particle sinks and not on a decrease of the ionization source. For the rollover and the beginning of the partially detached phase, the particle losses by perpendicular transport and the molecular activated recombination processes are mainly involved. For a deeper detachment with significant target ion flux reduction, volume recombination appears to be the main contributor. The elastic molecule-ion collisions are also important to provide good neutral confinement in the divertor and thus stabilize the simulations at low electron temperature (T e), when the sink terms are strong. Comparison between EDGE2D-EIRENE and SOLPS4.3 simulations of the density ramp in C shows similar detachment trends, but the importance of the elastic ion-molecule collisions is reduced in SOLPS4.3. Both codes suggest that any process capable of increasing the neutral confinement in the divertor should help to improve the modelling of the detachment. A further outcome of this work has been to demonstrate that key JET divertor diagnostic signals—Langmuir probe T e and bolometric tomographic reconstructions—are running beyond the limit of validity in high recycling and detached conditions and cannot be reliably used for code validation. The simulations do, however, reproduce the trend of the evolution of the line integrated bolometer chord measurements. The comparison between the code results and high-n Balmer line radiation intensity profiles confirms that a strong volume recombination is present during the experimental detachment and may play a role in this process, as suggested by the code.