We present experimental results on the counting rate measurements for several single-gap 10B lined resistive plate chambers (10B-RPCs) with anodes made from standard float glass, low-resistivity glass and ceramic. The measurements were performed at the V17 monochromatic neutron beamline (3.35 Å) at the Helmholtz-Zentrum Berlin. For the 10B-RPCs with 0.28mm thick float glass a maximum counting rate density of about 8 × 103 Hz/cm2 was obtained. In the case of low resistivity glass and ceramic, the counting rate density did not deviate from linear dependence on the neutron flux up to the maximum flux available at this beamline and exceeded a value of 3 × 104 Hz/cm2.