We present UBVRI light curves of BL Lacertae from May 2000 to January 2001, obtained by 24 telescopes in 11 countries. More than 15 000 observations were performed in that period, which was the extension of the Whole Earth Blazar Telescope (WEBT) campaign originally planned for July-August 2000. The exceptional sampling reached allows one to follow the flux behaviour in fine detail. Two different phases can be distinguished in the light curves: a first, relatively low-brightness phase is followed by an outburst phase, after a more than 1 mag = brightening in a few weeks. Both the time duration (about 100 d) and the variation amplitude (roughly 0.9 mag) are similar in the two phases. Rapid flux oscillations are present all the time, involving variations up to a few tenths of mag on hour time scales, and witnessing an intense intraday activity of this source. In particular, a half-mag brightness decrease in about 7 h was detected on August 8-9, 2000, immediately followed by a ~ 0.4 mag brightening in 1.7 h. Colour indexes have been derived by coupling the highest precision B and R data taken by the same instrument within 20 min and after subtracting the host galaxy contribution from the fluxes. The 620 indexes obtained show that the optical spectrum is weakly sensitive to the long-term trend, while it strictly follows the short-term flux behaviour, becoming bluer when the brightness increases. Thus, spectral changes are not related to the host galaxy contribution, but they are an intrinsic feature of fast flares. We suggest that the achromatic mechanism causing the long-term flux base-level modulation can be envisaged in a variation of the relativistic Doppler beaming factor, and that this variation is likely due to a change of the viewing angle. Discrete correlation function (DCF) analysis reveals the existence of a characteristic time scale of variability of ~ 7 h in the light curve of the core WEBT campaign, while no measurable time delay between variations in the B and R bands is found.