  We consider a sample of 107 Gamma Ray Bursts (GRBs) for which early UV
emission was measured by Swift, and extrapolate the photon intensity to lower
energies. Protons accelerated in the GRB jet may interact with such photons to
produce charged pions and subsequently ultra high energy neutrinos
$\varepsilon_\nu\geq 10^{16}$ eV. We use simple energy conversion efficiency
arguments to predict the maximal neutrino flux expected from each GRB. We
estimate the neutrino detection rate at large area radio based neutrino
detectors and conclude that the early afterglow neutrino emission is too weak
to be detected even by next generation neutrino observatories.
