A novel frequency modulation scheme has been developed for the multi-channel reflectometer used to measure density profiles and density fluctuations on the JET tokamak. This reflectometer normally uses slow frequency sweeping, combined with fixed-frequency operation, to measure the group delay, as well as plasma fluctuations, at 10 different microwave frequencies. The novel scheme uses continuous frequency modulation on a time-scale much faster than that of plasma fluctuations, the main aim being to make the group delay measurement more robust against plasma fluctuations. This paper discusses the theoretical background of the scheme, gives a detailed description of the system, and presents results from plasma measurements.