Since the electricity market liberalisation of the mid-1990s, forecasting energy demand and prices in competitive markets has become of primary importance for energy suppliers, market regulators and policy makers. In this paper, we propose a non-parametric model to obtain point and interval predictions of price and demand. It does not require any parametric assumption on the distribution of the error term or on the functional relationships linking the response variable to covariates. The assumed location–scale model provides a non-parametric estimation of the conditional mean and of the conditional variance by means of a Generalised Additive Model. Interval forecasts, at any given confidence level, are then obtained using a further non-parametric estimation of the innovation’s quantile. Since both the conditional mean and the conditional variance of the response variable are non-linear functions of covariates depending on calendar factors, renewable energy productions and other market variables, the resulting model is very flexible. It easily adapts to market conditions as well as to the non-linear characteristics of demand, supply and prices. An application to hourly data for the Italian electricity market, over the period 2015–2019 period, shows the one-day-ahead forecasting performance of the model for zonal electricity prices and level of demand.