To go back somewhat: Two new groups of people emerged in Central Europe around about the late Neolithic period. Each group may be identified independently by their respective burial sites.
The first is the so-called Beaker folk, buried with their Bell Beaker-shaped drinking vessels; the second the "Battle-Axe" folk. It is thought that they may have originated in the Middle East, perhaps as far as present day Iran, and as separate peoples. In Central Europe, by about the beginning of the second millenium, they have fused to become one European people, though with varying cultures. Shortly afterwards, the Bronze age began.
Three successive cultures appear: the first, the Unêtice appear to be the original fusing of the Beaker and the Battle-Axe folk. The Tumulus culture followed the Unêtice, and they are distinguished, as the name implies, by their manner of burying their dead beneath burial mounds. These are to be found throughout Europe, and the British Isles, , and are found also, scattered through Northern and Northwest Spain, and Northern and Central Portugal.
The next group to follow we know as the Urnfeld culture. Some scholars have identified these people as "Proto-Celtic" in that they may have spoken an early form of that language. These people cremated their dead and placed the remains in urns which were buried in flat cemeteries without any covering mound. Like the Tumulus people before them, this period of prehistory shows a great deal of expansion with trade to the south east and later the south west.
It is during the period of the Urnfeld people that agriculture begins to thrive in south and central Europe. This was the time that the Bronze Age was at its peak. Archaeological evidence shows that they produced weapons, tools, eating and cooking vessels, etc.
By the time of the Hallstatt people (named after the town of Hallstatt in Austria where large archaeological finds have been made), and La Tene people, (named likewise after an area in western Switzerland), we find tribes who are considered fully Celtic. Their culture stretched from approximately 1200 BCE to 500 BCE, and it is the very central period which is of interest to us, for this is the period that they began to cross the western passes of the Pyrenees. Many historians argue that the Halstatt people, from whom we derive the idea of "Celtishness” may have penetrated as far as Britain, and possibly later into Ireland through Wales, but by the time they did so, those who had moved towards the Iberian peninsula had long gone.
These people that entered the Western passes through the Pyrenees appear to be an earlier group. It is thought that they did so as early as 1100 BCE. That they left a strong impression upon Iberia, especially in the north, there is no doubt.