Abstract We develop a set of machine-learning based cosmological emulators, to obtain fast model predictions for the C(ℓ) angular power spectrum coefficients, characterising tomographic observations of galaxy clustering and weak gravitational lensing from multi-band photometric surveys (and their cross-correlation). A set of neural networks are trained to map cosmological parameters into the coefficients, achieving, with respect to standard Boltzmann solvers, a speed-up of $\mathcal {O}(10^3)$ in computing the required statistics for a given set of cosmological parameters, with an accuracy better than 0.175% (<0.1% for the weak lensing case). This corresponds to $\lesssim 2~{{\%}}$ of the statistical error bars expected from a typical Stage IV photometric surveys. Such overall improvement in speed and accuracy is obtained through (i) a specific pre-processing optimisation, ahead of the training phase, and (ii) an effective neural network architecture. Compared to previous implementations in the literature, we achieve an improvement of a factor of 5 in terms of accuracy, while training a considerably lower amount of neural networks. This results in a cheaper training procedure and a higher computational performance. Finally, we show that our emulators can recover unbiased posteriors when analysing synthetic Stage-IV galaxy survey datasets.