So far, no cases of the equivalent of mad cow disease have been discovered in sheep and there is currently no suggestion that infection will break out.
But the government has issued a contingency plan in case infection occurs in the future, to avoid being "wrong-footed" as happened over BSE.
The plan includes a worst-case scenario in which the eating of lamb would be banned, and the entire UK flock of up to 40 million sheep would be destroyed.
The whole programme would be 10 times the size of the foot-and-mouth slaughter.
Agriculture minister Eliot Morley said it was only fair that the public were aware of what contingency planning had been made.
"In the past, there is no doubt in my mind that information like this would have been very tightly suppressed because of the fears of food scares. But we should trust the public.
Phillips' report
"You have to look at the absolute worst-case scenario, and it is fair to say that the idea of slaughtering the whole UK flock is at the very extreme end of that."
The decision to publish the action plan was a response to a key criticism in Lord Phillips' report on the BSE crisis, published in October 2000.
It said ministers in the previous Conservative government had failed to think the unthinkable - that the fatal cattle disease might spread to humans.
When the unthinkable happened, in 1996, the government was "wrong-footed", and the result was panic, said the report.
The current government stresses there is no suggestion the national flock will become infected with BSE, but says it is now thinking the unthinkable, and sharing its thoughts with the public.
Theoretical possibility
The plan warns that there is a theoretical possibility that BSE could be passed to, and among, sheep.
It says that in sheep, BSE would appear to behave like the sheep disease scrapie and therefore could be passed between animals in the same way.
Mr Morley told an earlier news conference: "Sheep have been given BSE by feeding them infected BSE brain tissue.
"So, if it can be done under laboratory conditions, we have to take the precautionary principle and look for the possibility that it is in the national flock."
A surveillance programme is actively looking for signs of BSE in the national flock, by testing the brains of sheep with scrapie.
However, it has not so far been possible to sample large numbers of sheep.
The plan states the reason for this "is because of the probable under-reporting of scrapie".
"Not all reported cases are suitable for testing and the rapid biochemical methods of differentiating between BSE and scrapie have not been sufficiently well developed to distinguish between BSE and some strains of scrapie."
No evidence
National Farmers' Union Deputy President Tim Bennett told BBC News 24 he was "hopeful" that BSE would never be found in sheep.
"We have been looking since the 1980s to see if BSE is in sheep and we have found no evidence whatsoever.
"We are hopeful that we will never find it in sheep but it's important we have a contingency plan just in case.
"Sheep eat very little feed - they would have been exposed to very little or none of the exposed feed in the 1980s."
Mr Bennett said if BSE was found the consequences of the slaughter would be catastrophic.
"It would wipe out the hill and uplands of this country."