The plant has at least one inlet (2) for the effluent to be treated, an evaporator (6) for at least part of the water content, converting the effluent into steam and solids or paste material, with outlets (8, 10) for the steam and water, and an incinerator (14) for reducing the remaining solids or paste material into cinders. The incinerator is located beneath the evaporator so that surplus energy from the combustion of solids and paste material is used to evaporate the water. The liquid effluent is heated before it enters the evaporator by means of a heat exchanger (4) fed by the steam, with water condensed by the heat exchanger passing through outlet (10).