Forests are major carbon stores on a global scale but there are significant uncertainties about changes in carbon flux through time and the relative contributions of drivers such as land use, climate and atmospheric CO₂. We used the dynamic vegetation model LPJ-GUESS to test the relative influence of CO₂ increase, temperature increase and management on carbon storage in living biomass in an unmanaged European temperate deciduous forest. The model agreed well with living biomass reconstructed from forest surveys and maximum biomass values from other studies. High-resolution climate data from both historical records and general circulation models were used to force the model and was manipulated for some simulations to allow relative contributions of individual drivers to be assessed. Release from management was the major driver of carbon storage for most of the historical period, whereas CO₂ took over as the most important driver in the last 20 years. Relatively, little of the observed historical increase in carbon stocks was attributable to increased temperature. Future simulations using IPCC RCP4.5 and RCP8.5 scenarios indicated that carbon stocks could increase by as much as 3 kg C m⁻² by the end of the century, which is likely to be driven by CO₂ increase. This study suggests that unmanaged semi-natural woodland in Europe can be a major potential carbon sink that has been previously underestimated. Increasing the area of unmanaged forest would provide carbon sink services during recovery from timber extraction, while long-term protection would ensure carbon stocks are maintained.