We analyse new genomic data (0.05-2.95x) from 14 ancient individuals from Portugal distributed from the Middle Neolithic (4200-3500 BC) to the Middle Bronze Age (1740-1430 BC) and impute genomewide diploid genotypes in these together with published ancient Eurasians. While discontinuity is evident in the transition to agriculture across the region, sensitive haplotype-based analyses suggest a significant degree of local hunter-gatherer contribution to later Iberian Neolithic populations. A more subtle genetic influx is also apparent in the Bronze Age, detectable from analyses including haplotype sharing with both ancient and modern genomes, D-statistics and Y-chromosome lineages. However, the limited nature of this introgression contrasts with the major Steppe migration turnovers within third Millennium northern Europe and echoes the survival of non-Indo-European language in Iberia. Changes in genomic estimates of individual height across Europe are also associated with these major cultural transitions, and ancestral components continue to correlate with modern differences in stature.