This work presents experiments and modelling of OH densities in a radio-frequency driven atmospheric-pressure plasma in a plane-parallel geometry, operated in helium with small admixtures of oxygen and water vapour (He + O2 + H2O). The density of OH is measured under a wide range of conditions by absorption spectroscopy, using an ultra-stable laser-driven broad-band light source. These measurements are compared with 0D plasma chemical kinetics simulations adapted for high levels of O2 (1%). Without O2 admixture, the measured density of OH increases from 1.0 × 1014 to 4.0 × 1014 cm−3 for H2O admixtures from 0.05% to 1%. The density of atomic oxygen is about 1 × 1013 cm−3 and grows with humidity content. With O2 admixture, the OH density stays relatively constant, showing only a small maximum at 0.1% O2. The simulations predict that the atomic oxygen density is strongly increased by O2 addition. It reaches ~1015 cm−3 without humidity, but is limited to ~1014 cm−3 beyond 0.05% water content. The addition of O2 has a weak effect on the OH density because, while atomic oxygen becomes a dominant precursor for the formation of OH, it makes a nearly equal contribution to the loss processes of OH. The small increase in the density of OH with the addition of O2 is instead due to reaction pathways involving increased production of HO2 and O3. The simulations show that the densities of OH, O and O3 can be tailored relatively independently over a wide range of conditions. The densities of O and O3 are strongly affected by the presence of small quantities (0.05%) of water vapour, but further water addition has little effect. Therefore, a greater range and control of the reactive species mix from the plasma can be obtained by the use of well-controlled multiple gas admixtures, instead of relying on ambient air mixing.