The change from a hunter-gatherer to a farming way of life is what defines the start of the Neolithic or New Stone Age. In Britain the preceding period of the last, post-glacial hunter-gatherer societies is known as the Mesolithic, or Middle Stone Age.
It used to be believed that the introduction of farming into Britain was the result of a huge migration or folk-movement from across the Channel. Today, studies of DNA suggest that the influx of new people was probably quite small - somewhere around 20% of the total population were newcomers.