Since the launch of the Fermi satellite, BL Lacertae has been moderately active at gamma-rays and optical frequencies until May 2011, when the source started a series of strong flares. The exceptional optical sampling achieved by the GLAST-AGILE Support Program (GASP) of the Whole Earth Blazar Telescope (WEBT) in collaboration with the Steward Observatory allows us to perform a detailed comparison with the daily gamma-ray observations by Fermi. Discrete correlation analysis between the optical and gamma-ray emission reveals correlation with a time lag of 0 +- 1 d, which suggests cospatiality of the corresponding jet emitting regions. A better definition of the time lag is hindered by the daily gaps in the sampling of the extremely fast flux variations. In general, optical flares present more structure and develop on longer time scales than corresponding gamma-ray flares. Observations at X-rays and at millimetre wavelengths reveal a common trend, which suggests that the region producing the mm and X-ray radiation is located downstream from the optical and gamma-ray-emitting zone in the jet. The mean optical degree of polarisation slightly decreases over the considered period and in general it is higher when the flux is lower. The optical electric vector polarisation angle (EVPA) shows a preferred orientation of about 15 deg, nearly aligned with the radio core EVPA and mean jet direction. Oscillations around it increase during the 2011-2012 outburst. We investigate the effects of a geometrical interpretation of the long-term flux variability on the polarisation. A helical magnetic field model predicts an evolution of the mean polarisation that is in reasonable agreement with the observations. These can be fully explained by introducing slight variations in the compression factor in a transverse shock waves model. ; Comment: 17 pages, 17 figures, 1 table, accepted for publication in MNRAS