Archaeologists disagree about how farming began in Britain. Some argue it was a result of indigenous groups adopting domesticates and cultigens via trade and exchange. Others contend it was the consequence of a migration of farmers from mainland Europe. To shed light on this debate, we used radiocarbon dates to estimate changes in population density between 8000 and 4000 cal BP. We found evidence for a marked and rapid increase in population density coincident with the appearance of cultigens around 6000 cal BP. We also found evidence that this increase occurred first in southern England and shortly afterwards in central Scotland. These findings are best explained by groups of farmers from the Continent independently colonizing England and Scotland, and therefore strongly support the migrant farmers hypothesis.