Measurements of particle-recoil coincidences in low-energy (p,α) reactions on 6,7Li, 15N, 19F and 23Na target nuclei are described. Reaction α-particles were detected using a silicon surface-barrier detector, while the corresponding recoil nuclei were measured with a microchannel plate detector. Absolute microchannel plate detection efficiencies for a range of recoil energies (0.3- 8.3 MeV) and masses ( A=3-20) are presented. The dependence of the microchannel plate detection efficiency on increasing background count rates is investigated. The usefulness of the present experimental technique for investigations of interest to nuclear astrophysics is discussed.