23 pages, 8 figures.Searching for the Ultra high energy Cosmic rays and Neutrinos of $> 10^{20} eV$ is of great cosmological importance. A powerful technique is to search for the \v{C}erenkov radio emission caused by UHECR or UHE neutrinos impinging on the lunar regolith. We examine in this paper feasibility of detecting these events by observing with the Giant Metrewave Radio Telescope (GMRT) which has a large collecting area and operates over a wide frequency range with an orthogonal polarisation capability. We discuss here prospects of observations of the \v{C}erenkov radio emission with the GMRT at 140 MHZ with 32 MHz bandwidth using the incoherent array and also forming 25 beams of the Central Array to cover the moon. We also consider using the Ooty Radio Telescope (ORT) which was specially designed in 1970 for tracking the Moon. With the ORT (530m long and 30m wide parabolic cylinder) it becomes possible to track the Moon for 9.5 hours on a given day by a simple rotation along the long axis of the parabolic cylinder. ORT operates at 325 MHz and has an effective collecting area of ~ 8000 $m^2.$ Recently a digital system has been installed by scientists of the Raman Research Institute (RRI), Bangalore and the Radio Astronomy Centre (RAC) of NCRA/TIFR, at Ooty allowing a bandwidth of 10 MHz with ~ 40 ns sampling. It is possible to form 6 beams covering the Moon and 7th beam far away for discrimination of any terrestrial RFI. Increasing the bandwidth of the existing 12 beam analogue system of the ORT from 4 MHz to 15 MHz to be sampled digitally is planned. It is shown that by observing the Moon for $\ge$ 1000 hrs using the ORT it will provide appreciably higher sensitivity than past searches made elsewhere. Using the GMRT and ORT, it may be possible to reach sensitivity to test the Waxman-Bachall limit on UHE neutrino flux.The work of S.P. was supported by the Ministerio de Educación y Ciencia under Proyecto Nacional FPA2006-01105, and also by the Comunidad de Madrid under Proyecto HEPHACOS, Ayuda de I+D S-0505/ESP-0346.Peer reviewed