They say the findings increase concern that "a large section of the UK population may be at considerable risk" after having eaten infected beef.
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He said there was still much to learn about Creutzfeldt-Jakob (vCJD) disease - the illness linked to BSE - and how many people might eventually die, but he warned that the consequences could be "frightening".
Frances Hall, from the Human BSE Foundation, which supports families affected by vCJD, said it would be of some comfort to know where the disease had come from.
"Some people have tried to deny this link, but this study confirms it."
Two-year inquiry
Researchers from both the US and the UK were involved in the study. They have established that the same type of infectious agent, or prion, is responsible for both BSE in cows and the new form of Creutzfeldt-Jakob (vCJD) disease in humans that has struck down at least 48 people.
Winding up the public hearings on Friday, Lord Phillips also warned that the number of people who have already died from eating infected meat products in Britain could be just the "tip of the iceberg".
Professor Liam Donaldson, the chief medical officer, said: "There is still a lot of uncertainty about this disease, but we are not going to know for several years whether the size of the epidemic will be a small one - in the hundreds - or a very large one - in the hundreds of thousands."
The crisis resulted in the wholesale slaughter of thousands of cows and a beef export ban.
Species barrier
Most experts believe that the sudden appearance of vCJD in 1996 - a disease that causes sponge-like holes in the brain - has its origins in diseased cattle.
They hypothesised that both BSE and vCJD were caused by rogue prion proteins that jumped the species barrier from cows into humans. But although various studies have appeared to support this linkage, conclusive proof has remained elusive.
Now researchers from the University of California, San Francisco, and the UK National CJD Surveillance Unit, Scotland, have reported striking similarities between the two diseases. The scientists conducted experiments with mice genetically-altered to produce the same prions naturally found in cows.
They discovered, not unexpectedly, that there was no species barrier between the mice and cows. Diseased brain tissue injected into the mice produced symptoms in 250 days, the same incubation period experienced by cattle with BSE.
A second group of mice given prions from the first group also became sick in virtually the same period of time. But the big surprise came when human brain tissue infected with the prions that cause vCJD was injected into the mice.
'Indistinguishable' identities
Once again there was no apparent sign of a species barrier, but, more significantly, vCJD had virtually the same incubation period in the mice as BSE.
The pattern of brain damage was also identical. The results suggest that BSE and vCJD are interchangeable. Introduced into transgenic mice, vCJD prions assumed an identity "indistinguishable from BSE prions", the researchers write in the PNAS.
The similarities not only force the scientists to the conclusion that BSE must be the cause of vCJD, but make them worry that many more people than previously thought could fall ill as a result of eating infected meat.
The research team also found their altered mice were highly susceptible to infection with the sheep prion disease scrapie, although this produced a different biological pattern.
Scientists suspect BSE may have originated in cattle as a result of feeding them sheep remains infected with scrapie. The transgenic mice used in this study could be used to check this linkage, the team say.