Detailed electron density profiles of the scrape-off layer in high-performance JET plasmas (plasma current, I-p < 5 MA, neutral beam heating power, P-nbi similar to 17 MW) have been measured by means of a lithium beam diagnostic system featuring high spatial resolution [K. Kadota et al., Plasma Phys. Controlled Fusion 20 (1978) 1011]. Measurements were taken over a period of several seconds, allowing examination of the evolution of the edge profile at a location upstream from the divertor target. The data clearly show the effects of the H-mode transition - an increase in density near the plasma separatrix and a reduction in density scrape-off length. The profiles obtained under various plasma conditions are compared firstly with data from other diagnostics, located elsewhere in the vessel, and also with the predictions of an 'onion-skin' model (DIVIMP), which used, as initial parameters, data from an array of probes located in the divertor target.