Based on the work by Mitra, Choudhury & Ferrara, we obtain model-independent constraints on reionization from cosmic microwave background (CMB) and QSO absorption line data by decomposing the function Nion(z) (the number of photons entering the intergalactic medium per baryon in collapsed objects) into its principal components. The main addition in this work is that for the CMB data set, we explicitly include the angular power spectra Cl for TT, TE and EE modes in our analysis which seem to contain somewhat more information than taking the electron scattering optical depth τel as a single data point. Using Markov chain Monte Carlo methods, we find that all the quantities related to reionization can be severely constrained at z < 6 whereas a broad range of reionization histories at z > 6 are still permitted by the current data sets. With currently available data from WMAP7, we constrain 0.080 < τel < 0.112 (95 per cent CL) and also conclude that reionization is 50 per cent complete for (95 per cent CL) and is 99 per cent complete for (95 per cent CL). With the forthcoming Planck data on large-scale polarization (ignoring the effect of foregrounds), the z > 6 constraints will be improved considerably, e.g. the 2σ error on τel will be reduced to 0.009 and the uncertainties on and will be ∼1 and 3 (95 per cent CL), respectively. For more stringent constraints on reionization at z > 6, one has to rely on data sets other than the CMB. Our method will be useful in such a case since it can be used for non-parametric reconstruction of the reionization history with arbitrary data sets.