A microwave interferometry technique is applied for the first time for detecting a discrete spectrum of Alfvén Cascade (AC) eigenmodes excited with fast ions in reversed magnetic shear plasmas of the Joint European Torus (JET). The interferometry measurements of plasma density perturbations associated with ACs show an unprecedented frequency and time resolution of the eigenmodes superior to that obtained with external magnetic coils and with the electron-cyclotron emission radiometer. With the new technique, the spectrum of ACs is observed under a broader variety of conditions including plasmas with neutral beam injection, toroidally rotating plasmas and plasmas with toroidal current holes. The time-resolved measurements of ACs are used for monitoring the evolution of the safety factor and the density of rational magnetic surfaces in the region of maximum plasma current. The data obtained is used for developing reliable and reproducible scenarios with internal transport barriers on JET and provides an essential basis for assessing similar diagnostic technique in next-step fusion machines such as ITER.