Abstract: Nuclear structure calculations in the context of a novel hybrid nuclear model, combining the nuclear shell model and the microscopic quasiparticle-phonon model are presented. The predictivity of the hybrid model is tested by computing inelastic neutral-current neutrino-nucleus scattering cross sections off the stable thallium isotopes. The cross sections are presented in terms of the incoming neutrino energy, taking also into account the effect of nuclear recoil energy. Also reported are the expected event rates assuming neutrinos emerging from pion-decay at rest and the diffuse supernova neutrino background. Regarding solar neutrino rates, new results are presented in the context of the hybrid model and compared with previously reported results based solely on nuclear shell model calculations, demonstrating the improved accuracy of the adopted hybrid model at higher neutrino energies.