Climate models can produce accurate representations of the most important modes of climate variability, but they cannot be expected to follow their observed time evolution. This makes direct comparison of simulated and observed variability difficult and creates uncertainty in estimates of forced change. We investigate the role of three modes of climate variability, the North Atlantic Oscillation, El Niño–Southern Oscillation and the Southern Annular Mode, as pacemakers of climate variability since 1781, evaluating where their evolution masks or enhances forced climate trends. We use particle filter data assimilation to constrain the observed variability in a global climate model without nudging, producing a near-free-running model simulation with the time evolution of these modes similar to those observed. Since the climate model also contains external forcings, these simulations, in combination with model experiments with identical forcing but no assimilation, can be used to compare the forced response to the effect of the three modes assimilated and evaluate the extent to which these are confounded with the forced response. The assimilated model is significantly closer than the “forcing only” simulations to annual temperature and precipitation observations over many regions, in particular the tropics, the North Atlantic and Europe. The results indicate where initialised simulations that track these modes could be expected to show additional skill. Assimilating the three modes cannot explain the large discrepancy previously found between observed and modelled variability in the southern extra-tropics but constraining the El Niño–Southern Oscillation reconciles simulated global cooling with that observed after volcanic eruptions.