We discuss constraints on cosmic reionisation and their implications on a cosmic star formation rate (SFR) density ρSFR model; we study the influence of key-parameters such as the clumping factor of ionised hydrogen in the intergalactic medium (IGM) CH II and the fraction of ionising photons escaping star-forming galaxies to reionise the IGM fesc. Our analysis has used SFR history data from luminosity functions, assuming that star-forming galaxies were sufficient to lead the reionisation process at high redshift. We have added two other sets of constraints: measurements of the IGM ionised fraction and the most recent result from Planck Satellite about the integrated Thomson optical depth of the cosmic microwave background τPlanck. Our analysis shows that a reionisation beginning as early as z ≥ 14 and persisting until z ~ 6 is a likely scenario. We also considered various possibilities for the evolution of fesc and CH II with redshift, and confront them with observational data cited above. We conclude that, if the model of a constant clumping factor is chosen, the fiducial value of three is consistent with observations; even if a redshift-dependent model is considered, the resulting optical depth is strongly correlated with CH II mean value at z > 7, an additional argument in favour of the use of a constant clumping factor. Similarly, a constant value of the escape fraction is favoured over a redshift-dependent model. When added as a fit parameter, we find fesc = 0.19 ± 0.04. However, this result strongly depends on the choice of magnitude limit in the derivation of ρSFR. Our fiducial analysis considers faint galaxies (Mlim = −13) and the result is a well constrained escape fraction of about 0.2, but when Mlim = −17, the number of galaxies available to reionise the IGM is not sufficient to match the observations, so that much higher values of fesc, approaching 70%, are needed.