This paper analyses the impact of the control measures during the COVID-19 lockdown in Europe (15 March-30 April 2020) on 1-h daily maximum nitrogen dioxide (NO2) and maximum daily 8-h running average ozone (MDA8 O3) observations obtained from the European Environment Agency's air quality database (AirBase). Daily maximum NO2 decreased consistently over the whole continent, with relative reductions ranging from 5% to 55% with respect to the same period in 2015-2019 for 80% of the sites considered (10th - 90th percentiles). However, MDA8 O3 concentrations showed a different pattern, decreasing over Iberia and increasing elsewhere. In particular, a large region from northwestern to central Europe experienced increases of 10-22% at urban background stations, reaching typical values of the summer season. The analysis of the expected NO2 and O3 concentrations in the absence of the lockdown, using generalised additive models fed by reanalysis meteorological data, shows that the low NO2 concentrations were mostly attributed to the emission reductions while O3 anomalies were dominated by the meteorology. The relevance of each meteorological variable depends on the location. The positive O3 anomalies in northwestern and central Europe were mostly associated with elevated temperatures, low specific humidity and enhanced solar radiation. This pattern could be an analogue to study the limits of pollution control policies under climate change scenarios. On the other hand, the O3 reduction in Iberia is mostly attributable to the low solar radiation and high specific humidity, although the reduced zonal wind also played a role in the proximity of the Iberian Mediterranean coast.