Results are presented of transport studies conducted on trace impurities injected with the laser blow-off technique in a variety of JET L mode pulses. In the core of the discharge, the transport is much slower, the impurity diffusion coefficient D is more than an order of magnitude below the values it assumes further out, but still above the neoclassical predictions. The extent of the slow transport core region varies with the magnetic field and with the total plasma current and is broadly correlated with the edge value of the safety factor. Closer analysis reveals that the current profile is essential in determining the radial dependence of D. This parameter appears to undergo a rapid transition to highly anomalous levels in the vicinity of the radial position where the dimensionless shear parameter is equal to 0.5. Within that region D stays moderate even when the electron temperature gradient is high. A marked increase of D in the outer region of the discharge is observed when the power per particle is raised or, alternatively, when the temperature and its gradient grow in that region, but no clear dependence of D on plasma density is found when the electron temperature profile is kept constant. Transport modelling based on the critical Del Tc assumption leads to D profiles that are similar, although not in detailed quantitative agreement, to the experimental ones when the temperature profiles are flat in the centre; when the temperature profiles are peaked in the centre, even the radial dependence of the predicted diffusion profiles is very different from the one observed. Recent theoretical attempts to analyse the radial structure of the microturbulent fluctuations predict a strong positive dependence of anomalous diffusion on the magnetic shear as observed in our experiments