No cases of the so-called mad cow disease have been observed in sheep.
But scientists believe it is possible that some cases of the disease may have been mistaken for the related sheep disease scrapie.
Basing its calculations on the number of cattle infected, a team from Oxford University has concluded that up to 1,500 sheep could have been infected in the late 1980s.
But the team, writing in the journal Science, said that even if BSE had spread to sheep, only a handful would have the disease now.
Test blunder
The first cases of Bovine Spongiform Encephalopathy (BSE) were seen in cattle at the end of 1984.
It is still not certain exactly how many cattle in the UK had the disease, but just over 1,000 suspected cases a week were being reported in the early 1990s.
It has been shown in laboratory conditions that BSE can be passed to sheep.
It is also known that sheep would have been exposed to some of the same infected feed that passed BSE to cattle during the 1980s.
Last month, a four-year study into whether sheep in the early 1990s had BSE was abandoned, after it emerged scientists had been testing material from cows' brains by mistake.
The government has since announced a programme of tests for more than 20,000 sheep brains for signs of BSE and scrapie.