We study, via a Monte Carlo simulation, a population of isolated asymmetric neutron stars where the magnitude of the magnetic field is low enough so that the dynamical evolution is dominated by the emission of gravitational waves. A starting population, with age uniformly distributed back to 100 Myr (or 500 Myr) and endowed with a birth kick velocity, is evolved in the Galactic gravitational potential to the present time. In describing the initial spatial distribution, the Gould belt, with an enhanced neutron star formation rate, is taken into account. Different models for the initial period distribution are considered. The star ellipticity, measuring the amount of deformation, is drawn from an exponential distribution. We estimate the detectability of the emitted gravitational signals by the first and planned second generation of interferometric detectors. Results are parametrized by the fraction of the whole galactic neutron star population made up of these kinds of sources. Some possible mechanisms, which would make possible the existence of such a population, are discussed. A comparison of the gravitational spin-down with the braking due to a possible interaction of the neutron star with the interstellar medium is also presented.