We present estimates of the photometric redshifts, stellar masses and star formation histories of sources in the Submillimetre Common-User Bolometer Array (SCUBA) HAlf Degree Extragalactic Survey (SHADES). This paper describes the 60 SCUBA sources detected in the Lockman Hole covering an area of similar to 320 arcmin(2). Using photometry spanning the B band to 8 mu m, we find that the average SCUBA source forms a significant fraction of its stars in an early period of star formation and that most of the remainder forms in a shorter more intense burst around the redshift it is observed. This trend does not vary significantly with source redshift. However, the sources show a clear increase in stellar mass with redshift, consistent with downsizing. In terms of spectral energy distribution types, only two out of the 51 sources we have obtained photometric redshifts for are best fitted by a quasar-like spectrum, with approximately 80 per cent of the sources being best fitted with late-type spectra (Sc, Im and starburst). By including photometry at 850 mu m, we conclude that the average SCUBA source is forming stars at a rate somewhere between 6 and 30 times the rate implied from the rest-frame optical in a dust obscured burst and that this burst creates 15-65 per cent of the total stellar mass. Using a simplistic calculation, we estimate from the average star formation history that between one in five and one in 15 bright (L-*+ 2 < L-optical < L-* - 1 mag) galaxies in the field over the interval 0 < z < 3 will at some point in their lifetime experience a similar energetic dusty burst of star formation. Finally, we compute the evolution of the star formation rate density and find it peaks around z similar to 2 .