The selective pressures that shape clonal evolution in healthy individuals are largely unknown. Here we investigate 8,342 mosaic chromosomal alterations, from 50 kb to 249 Mb long, that we uncovered in blood-derived DNA from 151,202 UK Biobank participants using phase-based computational techniques (estimated false discovery rate, 6-9%). We found six loci at which inherited variants associated strongly with the acquisition of deletions or loss of heterozygosity in cis. At three such loci (MPL, TM2D3-TARSL2, and FRA10B), we identified a likely causal variant that acted with high penetrance (5-50%). Inherited alleles at one locus appeared to affect the probability of somatic mutation, and at three other loci to be objects of positive or negative clonal selection. Several specific mosaic chromosomal alterations were strongly associated with future haematological malignancies. Our results reveal a multitude of paths towards clonal expansions with a wide range of effects on human health.