The Whole Earth Blazar Telescope (WEBT) collaboration has collected a large amount of optical and radio data on BL Lacertae in the last years, which, when added to literature data, allow to construct well-sampled light curves of the source from 1968 to the end of 2003. These optical and radio data are here analysed with three statistical methods designed for unevenly-sampled data trains in order to search for possible periodicities. While the main radio outbursts repeat every similar to 8 years, with a possible progressive stretching of the period, the evidence of an optical periodicity is much less clear. Radio light curves from 4.8 to 37 GHz are well correlated, with variations at the higher frequencies leading the lower-frequency ones by a few weeks for contiguous bands, up to a few months when considering the largest frequency separations. The radio behaviour reveals the presence of two different components, the softer-spectrum one constituting the bulk of the radio emission. On the other hand, the harder component shows itself as radio events which appear enhanced at the higher frequencies and seem to have optical counterparts. Cross-correlation between the optical light curve and radio hardness ratios indicates a radio time delay of more than 3 months. Thus, our analysis suggests a scenario where flux variations propagate towards less and less opaque regions, giving rise to related optical and hard radio events and, in more extended zones, to soft events apprently uncorrelated with the former ones.