Context. In the centre of pre-stellar cores, deuterium fractionation is enhanced due to low temperatures and high densities. Therefore, the chemistry of deuterated molecules can be used to probe the evolution and the kinematics in the earliest stages of star formation. Aims. We analyse the deuterium fractionation of simple molecules, comparing the level of deuteration in the envelopes of the prototypical pre-stellar core L1544 in Taurus and the young protostellar core HH211 in Perseus. Methods. We used single-dish observations of CCH, HCN, HNC, and HCO+ and their 13C-, 18O-, and D-bearing isotopologues, detected with the 20 m telescope at the Onsala Space Observatory. We derived the column densities, and subsequently the carbon isotopic ratios and deuterium fractions of the molecules. Additionally, we used radiative transfer simulations and results from chemical modelling to reproduce the observed molecular lines. We used new collisional rate coefficients for HNC, HN13C DNC, and DCN that consider the hyperfine structure of these molecules. Results. For CCH, we find high levels of deuteration (10%) in both sources, consistent with other carbon chains. We find moderate deuteration of HCN (5–7%), with a slight enhancement towards the protostellar core. Equal levels of deuteration for HNC towards both cores (~8%) indicate that HNC is tracing slightly different layers compared to HCN. We find that the deuterium fraction of HCO+ is enhanced towards HH211, most likely caused by isotope-selective photodissociation of C18O. With radiative transfer, we were able to reproduce the observed lines of CCH, HCN, H13CN HNC, HN13C and DNC towards L1544 as well as CCH, H13CN HN13C DNC, H13CO+ HC18O+ and DCO+ towards HH211. Conclusions. Similar levels of deuteration show that the deuterium fractionation is most probably equally efficient towards both cores, suggesting that the protostellar envelope still retains the chemical composition of the original pre-stellar core. The fact that the two cores are embedded in different molecular clouds also suggests that environmental conditions do not have a significant effect on the deuterium fractionation within dense cores. Our results highlight the uncertainties when dealing with 13C isotopologues and the influence of the applied carbon isotopic ratio. Radiative transfer modelling shows that it is crucial to include the effects of the hyperfine structure to reproduce the observed line shapes. In addition, to correctly model emission lines from pre-stellar cores, it is necessary to include the outer layers of the core to consider the effects of extended structures. In addition to HCO+ observations, HCN observations towards L1544 also require the presence of an outer diffuse layer where the molecules are relatively abundant.