The experimental determination of the relative biological effectiveness of thermal neutron factors is fundamental in Boron Neutron Capture Therapy. Present values have been obtained using mixed beams consisting of both neutrons and photons of various energies. A common weighting factor has been used for both thermal and fast neutron doses, although such an approach has been questioned. At the nuclear reactor of the Institut Laue-Langevin a pure low-energy neutron beam has been used to determine thermal neutron relative biological effectiveness factors. Different tumor cell lines, corresponding to glioblastoma, melanoma, and head and neck squamous cell carcinoma, and non-tumor cell lines (lung fibroblast and embryonic kidney) have been irradiated using an experimental arrangement designed to minimise neutron-induced secondary gamma radiation. Additionally, the cells were irradiated with photons at a medical linear accelerator, providing reference data for comparison with that from neutron irradiation. Survival and proliferation were studied after irradiation, yielding the Relative Biological Effectiveness corresponding to the damage of thermal neutrons for the different tissue types.