We present predictions for the structural and photometric properties of early-type galaxies in the Lambda cold dark matter (ΛCDM) cosmology from the published semi-analytical galaxy formation models of Baugh et al. and Bower et al. These calculations were made with the GALFORM code, which tracks the evolution of the disc and bulge components of a galaxy, using a self-consistent model to compute the scalelengths. The sizes of galactic discs are determined by the conservation of the angular momentum of cooling gas. The sizes of merger remnants are computed by applying the virial theorem and conserving the binding energy of the progenitors and their orbital energy. There are a number of important differences between the two galaxy formation models. To suppress the overproduction of bright galaxies, the Bower et al. model employs active galactic nuclei heating to stifle gas cooling, whereas the Baugh et al. model invokes a superwind which ejects cooled gas. Also, in the Baugh et al. model a top-heavy stellar initial mass function is adopted in starbursts. We compare the model predictions with observational results derived from the Sloan Digital Sky Survey. The model enjoys a number of notable successes, such as giving reasonable reproductions of the local Faber–Jackson relation (velocity dispersion–luminosity), the velocity dispersion–age relation, and the Fundamental Plane relating the luminosity, velocity dispersion and effective radius of spheroids. These achievements are all the more remarkable when one bears in mind that none of the parameters has been adjusted to refine the model predictions. We study how the residuals around the Fundamental Plane relation depend on galaxy properties. We examine in detail the physical ingredients of the calculation of galaxy sizes in GALFORM, showing which components have the most influence over our results. We also study the evolution of the scaling relations with redshift. However, in spite of the successes, there are some important disagreements between the predictions of the model and observations: the brightest model spheroids have effective radii smaller than observed and the zero-point of the Fundamental Plane shows little or no evolution with redshift in the model.