Early-type galaxies (ETGs) are thought to be devoid of dust and star-formation, having formed most of their stars at early epochs. We present the detection of the dustiest ETGs in a large-area blind submillimetre survey with Herschel (H-ATLAS, Eales et al.2010), where the lack of pre-selection in other bands makes it the first unbiased survey for cold dust in ETGs. The parent sample of 1087 H-ATLAS galaxies in this study have a ⩾ 5σ detection at 250μm, a reliable optical counterpart to the submillimetre source (Smith et al.2011) and a spectroscopic redshift from the GAMA survey (Driver et al.2011). Additionally, we construct a control sample of 1052 optically selected galaxies undetected at 250μm and matched in stellar mass to the H-ATLAS parent sample to eliminate selection effects. ETGs were selected from both samples via visual classifications using SDSS images. Further details can be found in Rowlands et al. (2012). Physical parameters are derived for each galaxy using the multiwavelength spectral energy distribution (SED) fitting code of da Cunha, Charlot and Elbaz (2008), Smith et al.2012, using an energy balance argument. We investigate the differences between the dusty ETGs and the general ETG population, and find that the H-ATLAS ETGs are more than an order of magnitude dustier than the control ETGs. The mean dust mass of the 42 H-ATLAS ETGs is 5.5 × 107M⊙ (comparable to the dust mass of spirals in our sample), whereas the dust mass of the 233 control ETGs inferred from stacking at optical positions on the 250μm map is (0.8 - 4.0) × 106M⊙ for 25-15 K dust. The average star-formation rate of the H-ATLAS ETGs is 1.0 dex higher than that of control ETGs, and the mean r-band light-weighted age of the H-ATLAS ETGs is 1.8 Gyr younger than the control ETGs. The rest-frame NUV - r colours of the H-ATLAS ETGs are 1.0 magnitudes bluer than the control ETGs, and some ETGs may be transitioning from the blue cloud to the red sequence. Some H-ATLAS ETGs show signs of morphological disturbance and may have undergone recent rejuvenation of their ISM via gas and dust delivered by mergers. It is found that late-type stars cannot produce enough dust to account for that observed in the H-ATLAS ETGs. This indicates that either an external source of dust from mergers is required, a substantial amount of dust grain growth must occur in the ISM, or dust destruction by hot X-ray gas is less efficient than predicted.