Human or proto-human history in Britain goes back a long way. Flint debris, teeth and a shin bone from near Chichester have been dated back half a million years. Neanderthal teeth from near Rhyl are maybe half that old. A mere 30,000 years ago, people much like us buried one of their number, "the Red Lady of Paviland" (he was actually a man), in a cave in south Wales.

Barry Cunliffe, then, has a great sweep to cover, which he does with usually unchallengeable authority. Yet most of the period of human inhabitation of Britain has little to do with who we are now. Some 13,000 years ago a dramatic drop in mean annual temperature  15C in the space of a single generation  drove even the hardy hunters of Paviland and points north out of Britain entirely. Humans made a new start only when the birch, pine and hazel woods began to recolonise the tundra, and it was these pioneers, Cunliffe points out, who were "the direct ancestors of the majority of the people" living in Britain and Ireland today.

They still had to cope with enormous upheavals, which dwarf modern fears of climate change. The melting ice separated Ireland from Britain, Britain from the Continent, and drowned "Doggerland", where hunters had roamed what is now the North Sea. A thick layer of sand along the east coast of Scotland bears witness to an ominously huge tsunami, perhaps connected to the drowning. Much more precisely datable, by tree-rings, to a mere 3,000 years ago, are the signs of a 20-year winter caused by volcanic ash. One has to wonder, could we cope with natural disasters such as this as well as our hunter-ancestors did?

And can we tell any more about our ancestors than that they were here? Our traditional narrative has long been that of invasions from the east and retreat to the west. So, in schoolbook history, the Goidelic Celts, arriving from Gaul, got pushed into Ireland by the Brythonic Celts, who were then pushed into Wales by the Anglo-Saxons, themselves displaced across the Danelaw by the Vikings.

Not much of this seems to be true. Cunliffe stresses "mobility, connectivity and the sea" as major themes, though he might well have added "continuity" to mobility. Much of our gene-pool, he thinks, comes from northern Iberia, to which the west of Britain and Ireland was more acessible than the east. He suggests that the Celtic languages also developed there, perhaps 5,000 years ago, became the lingua franca of the western sea-lanes, and then spread from the Atlantic seaboard.

Technology came along the same or similar routes. The inhabitants of Star Carr in Yorkshire were hunters, preying especially off the red deer whose skulls and antlers they made into headdresses. The middens of Oronsay and the Scottish west coast show reliance on shellfish and shallow-water fishing. Six thousand years ago, however, a neolithic agricultural revolution brought in crops and animal husbandry, along with flint mines and barrows and ambitious engineering, such as the Sweet Track across the Somerset marshes, which is datable by tree-rings to 3807-06BC.

The henges which are the most obvious memorial of this era were followed by copper technology, with the arsenical copper of Ross Island in County Kerry being mined around 2400BC, while the neolithic miners of Great Orme above Llandudno dug down more than 200ft for the new metal. Pure copper technology was soon supplanted by bronze made with British tin.

Were the new metal technologists immigrants or natives? The oxygen isotopes in the teeth of the "Amesbury Archer", buried in his richly furnished barrow on Boscombe Down, south of Stonehenge, show that he came from the Alps. But close by lies a younger man who shared the Archer's genetic anomaly, and he was born in Wessex. Stimulus from south and west, however, continued to be as important as cross-Channel migration. Cunliffe has a high opinion of the skin boats whose descendants survive as the tarred canvas curraghs of the Aran islands. The gold model of a 16-oar boat found in County Derry represents a craft that could easily have carried bulk cargo across the open sea.

It was new technology once again that led to the curraghs' slow replacement by plank boats whose timbers were held together by iron nails. There must have been many seafaring ventures of which we now know nothing. One mute testimony is the Roman pot dredged up from the Porcupine Bank, well out in the Atlantic, 150 miles west of Ireland. What was some skipper doing out there? Blown way off course? Or looking for more islands, like the Shetlands and Faroes and Iceland, all probably known and visited, if not always settled, well before the Christian era?

From about 1,500BC we enter the "Celtic" world described much later by Caesar as a kind of heroic age, with bronze swords and war-horns, gold torcs, cauldrons and spits and flesh-hooks for competitive feasting, and signs of "endemic warfare". On the Yorkshire Wolds men were buried in the much-prized war-chariots that so alarmed Caesar. In Hampshire and the south-west, hill-forts were burned, destroyed, rebuilt. Hundreds of examples have been found in Britain of a Gallo-Belgic coinage, which was made from as much as 10 tons of gold; the coins look like pay for British mercenaries, or perhaps loot.

Finally, there are the invasions for which we have some documentary evidence: good evidence for the Roman takeover in the first to fifth centuries AD, and again for the Viking incursions that began four centuries later, but with a major gap in between. This gap, of course, still creates a live political issue. Who are the English, how do they relate to the "Celtic fringe", and do they, indeed, ethnically exist?

Here Cunliffe grows wary, noting only that there is such a thing as "archaeological fashion" (which has recently tried to play down upheaval), while some aspects of the scant literary tradition (invasion, treachery, ethnic cleansing) do indeed find "strong support". DNA evidence has been of surprisingly little use, partly because of the "continuity" factor mentioned above  there are naturally more descendants of the people who got here first  and partly because it remains difficult to tell, for instance, fifth-century "Jutish" genes from ninth-century "Danish" ones.

Cunliffe's best guess is that the gene pool in south-east England got a 10-20% influx in the post-Roman period. Irish settlement in the west may have been just as genetically significant. The names "Déisi" and "Attacotti" (a Latin attempt at Irish "aithechtúatha") both mean "vassals", as if the Irish raiders, like Hengest's Jutes, were an originally displaced or subservient group looking for new opportunities.

That leaves aside two obvious questions, which are: how did the Anglian element succeed in establishing some kind of hegemony over the other Germanic groups, if only by title? (For even Alfred, king of the West Saxons, always called his own language englisc.) And how come 10-20% of fifth- or sixth-century immigrants imposed their language so comprehensively on the much larger proto-Welsh or vulgar Latin-speaking majority? Cultural loss of confidence on the one side? Cumulative breeding advantage on the other, caused by privileged access to indigenous females by a newly dominant male élite?

These are questions of mentalité, not readily accessible to students of material culture. When it comes to hard facts, Cunliffe has the data, and the often dramatically beautiful or startling photographs to give them life. His whole account must create a renewed respect for our British and Irish ancestors: all of them, wherever they came from, immigrants who became indigenous, and people who coped imaginatively with stress on a level we hope (but there's no telling) that we will never have to face again.

 Tom Shippey's JRR Tolkien: Author of the Century is published by HarperCollins.