A wide range of palaeoenvironmental evidence from the Holocene has suggested periodicities in the Earth's climate of 10s to 1000s of years. Identifying these millennial-, century- and decadal periodicities, and their impacts, is critical in developing a fuller understanding of natural climate variability. Any solar-induced climatic change needs to be distinguished from other causes of natural climate variability and from short-term catastrophic events induced either by external or internal processes. Such events might themselves generate a periodicity, or in combination with other forcing factors they may contribute towards a periodicity (and so spuriously imply a universal and continuing periodicity in the climate record), or they may resonate with a solar-induced periodicity. Here, evidence from peat records for periodicity in climate change over the mid to late Holocene is reviewed and this is followed by a test of the replicability of claimed periodicities using blanket peat data covering the past 2000 yr from four sites in the British Isles. Results suggest that the mires studied do go through phases of being responsive to periodic forcing factors, with ca. 200, ca. 80 and 60–50 yr wavelengths reflected in some data sets. However, the patterns shown are not consistent. This could be the result of local conditions at individual mires (human impact, sensitivity and vegetation succession) or of changes in the strength or nature of global forcing factors. Assessing a solar–mire link remains difficult because the century-scale variations of the Sun show different intervals between solar minima, the durations of which are themselves unequal, and because the proxy-climate data-sets from peat profiles may themselves not be dated with sufficient precision and/or accuracy. Copyright © 2001 John Wiley & Sons, Ltd.