The design and characterization of the coaxial dual-band L-P radio astronomical receiver for the prime focus of the Sardinia radio telescope are presented. The main feature of this receiver is to allow simultaneous radio astronomical observations in the P (305 -410 MHz) and L (1.3 -1.8 GHz) frequency bands. This functionality, which has been requested by the Pulsar research group at the National Institute for Astrophysics to estimate, among the others, the ionospheric dispersion in Pulsar observation, is currently missing in any other radio astronomical facility throughout the world. Also, single band operation is ensured by the proposed design both in linear and circular polarization, making this L-P receiver an ideal instrument for a wide range of radio astronomical and space applications. Some components of the receiver chain have been housed inside a cryostat and refrigerated at 20 K to reduce the noise temperature, resulting in a good performance compared to the receivers of other large radio telescopes. Several challenging issues have been faced in the design, mainly due to the large dimension and weight of the overall structure to be mounted in the prime focus position. Moreover, the design of the cryostat was constrained by the limited space available in the direction of the optical axis inside the focal cabin of the radio telescope, requiring a compact and light realization of the components of the receiver chain. This called for a home-made design of several devices, requiring a strong collaborative effort by researchers, engineers, and astronomers.