The wave was generated by a catastrophic subsea landslide off the coast of Norway.
Analysis suggests the tsunami over-ran Doggerland, a low-lying landmass that has since vanished beneath the waves.
“It was abandoned by Mesolithic tribes about 8,000 years ago, which is when the Storegga slide happened,” said Dr Jon Hill from Imperial College London.
The wave could have wiped out the last people to occupy this island.
The research has been submitted to the journal Ocean Modelling and is being presented at the European Geosciences Union General Assembly in Vienna this week.
Dr Hill and his Imperial-based colleagues Gareth Collins, Alexandros Avdis, Stephan Kramer and Matthew Piggott used computer simulations to explore the likely effects of the Norwegian landslide.
He told BBC News: “We were the first ever group to model the Storegga tsunami with Doggerland in place. Previous studies have used the modern bathymetry (ocean depth).”
As such, the study gives the most detailed insight yet into the likely impacts of the huge landslip and its associated tsunami wave on this lost landmass.
Some 8,200 years ago, an undersea slip generated a devastating tsunami
During the last Ice Age, sea levels were much lower; at its maximum extent Doggerland connected Britain to mainland Europe.
It was possible for human hunters to walk from what is now northern Germany across to East Anglia.
But from 20,000 years ago, sea levels began to rise, gradually flooding the vast landscape.
By around 10,000 years ago, the area would still have been one of the richest areas for hunting, fishing and fowling (bird catching) in Europe.
A large freshwater basin occupied the centre of Doggerland, fed by the River Thames from the west and by the Rhine in the east. Its lagoons, marshes and mudflats would have been a haven for wildlife.
“In Mesolithic times, this was paradise,” explained Bernhard Weninger, from the University of Cologne in Germany, who was not involved with the present study.
But 2,000 years later, Doggerland had become a low-lying, marshy island covering an area about the size of Wales.
Last year, National Museum of Antiquities curator Luc Amkreutz identified this flint tool as a Mesolithic tranchet axe – the first such find from the North Sea. It was found by a Dutch fisherman in 1988
The nets of North Sea fishing boats have pulled up a wealth of prehistoric bones belonging to the animals that once roamed this prehistoric “Garden of Eden”.
But the waters have also given up a smaller cache of ancient human remains and artefacts from which scientists have been able to obtain radiocarbon dates.
And they show that none of these relics of Mesolithic habitation on Doggerland occur later than the time of the tsunami.
The Storegga slide involved the collapse of some 3,000 cubic km of sediment.
“If you took that sediment and laid it over Scotland, it would cover it to a depth of 8m,” said Dr Hill.
Given that the majority of Doggerland was by this time less than 5m in height, it would have experienced widespread flooding.
“It is therefore plausible that the Storegga slide was indeed the cause of the abandonment of Doggerland in the Mesolithic,” the team writes in their Ocean Modelling paper.
Dr Hill told BBC News: “The impact on anyone who was living on Doggerland at the time would have been massive – comparable to the Japanese tsunami of 2011.”
But Bernhard Weninger suspects that Doggerland had already been vacated by the time of the Storegga slide.
“There may have been a few people coming with boats to fish, but I doubt it was continuously settled,” he explained.
“I think it was so wet by this time that the good days of Doggerland were already gone.”
Prof Vince Gaffney, an archaeologist at the University of Birmingham, said: “I think they (the researchers) are probably right, because the tsunami would have been a catastrophic event.”
But he stressed that the archaeological record was sparse, and explained that two axes from the Neolithic period (after Storegga) had been retrieved from the North Sea’s Brown Banks area.
It is possible these were dropped from a boat – accidentally or as a ritual offering – but it is also unclear precisely when Doggerland finally succumbed to the waves.
“Even after major volcanic eruptions, people go back, sometimes because they can’t afford not to but also because the resources are there,” said Prof Gaffney, who has authored a book, Europe’s Lost World: The Rediscovery of Doggerland.
The tsunami would also have affected what is now Scotland and the eastern coast of England, as well as the northern coast of continental Europe.
The wave that hit the north-east coast of Scotland is estimated to have been some 14m high, though it is unclear whether this area was inhabited at the time.
But waves measuring some 5m in height would have hit the eastern coast of England, and there is good evidence humans were in this area 8,000 years ago.
Much of this region would also have been low-lying, suggesting the impact on Mesolithic people who depended substantially on coastal resources such as shellfish, would have been significant here, too.