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 CHII withredshift,andconfrontthemwithobservationaldatacitedabove.Weconcludethat,ifthemodelofaconstantclumpingfactor is chosen, the fiducial value of three is consistent with observations; even if a redshift-dependent model is considered, the resulting opticaldepthisstronglycorrelatedwithCHII meanvalueatz>7,anadditionalargumentinfavouroftheuseofaconstantclumping 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.