Somatic mutations acquired in haematopoietic stem cells can drive clonal expansions, a phenomenon known as clonal haematopoiesis (CH). CH has been associated with higher risk of haematological cancer, cardiovascular disease and lower life expectancy and is strongly age-dependent, becoming almost ubiquitous in older adults. However, the dynamics of CH are not yet fully understood, and an accurate quantitative model of clonal expansion in healthy people could inform strategies for risk stratification and early detection of haematological malignancy. Here, we analyse the age-dependence of the variant allele frequency (VAF) distributions of CH driver variants from blood-derived whole exomes in 420,000 cancer-free UK Biobank participants. Across a number of CH driver genes (including DNMT3A, TP53 and TET2) we find evidence of a substantial deceleration of clonal expansion with age, while other drivers (including SRSF2, SF3B1, and IDH2) display more consistent growth throughout life. We find that this deceleration occurs consistently across the population and happens mostly before the age of 40. Using evolutionary models of clonal dynamics we assess the validity of alternative mechanisms of clonal deceleration. We find that variation in fitness among individuals (e.g. due to genetic susceptibility) is not sufficient to explain the deceleration. We also consider a clonal competition model in which clonal expansion later in life is inhibited by interference with a background of other expanding clones, and find this model inconsistent with the data given established estimates of the prevalence of hidden selection in blood. Our results imply that the intrinsic selection landscape in blood is substantially different in early life compared with middle age.