Lord Hunt said the investigation into the cluster included a large team of officials from bodies such as the National CJD Surveillance Unit in Edinburgh.
Professor Roy Anderson's comments come as inquiries continue into a cluster of deaths near the Leicestershire village of Queniborough.
The Department of Health is conducting research at Queniborough to determine if people in the area are more susceptible to the disease.
Three deaths have been linked to the village, according to local health authority officials.
Lord Hunt said the cases were unlikely to be a statistical quirk.
Epidemiologist Professor Roy Anderson told BBC Radio 4's World at One programme that the rate of CJD cases emerging in 2000 suggested that an epidemic of the disease was already under way in the UK.
When the first cases of the new variant disease came to light in 1995, there were three cases, followed by 10 in both 1996 and 1997 and 18 in 1998, he said.
Stark warning
Professor Anderson said: "This year, 2000, we have had 12 cases already and the total is likely to be greater than any previous year, so this epidemic is just starting.
"It may be a small epidemic, and all of us hope it will be, but this disease has such a long incubation period, where exposure was probably in the late 1980s, that it's far too early to say whether it will be small, medium or large."
The human form of BSE (bovine spongiform encephalopathy) claimed three lives in Leicestershire within 12 weeks in 1998.
Glen Day, 35, from Queniborough, and Pamela Beyless, 24, from nearby Glenfield, died in October. Stacey Robinson, 19, formerly of Queniborugh, died two months earlier in August.
A 19-year-old man died from the disease in May at the Leicester Royal Infirmary and, at the time, health officials said it was "highly probable" that a 24-year-old man in the county had also contracted it.
Lord Hunt said the investigation into the cluster included a large team of officials from bodies such as the National CJD Surveillance Unit in Edinburgh.
They will work closely with the Department of Health and the Ministry of Agriculture.
Support groups for CJD victims and their families have welcomed the investigation.
Clive Evers, chairman of the CJD Support Network, said: "We need more knowledge about CJD to see if there is some environmental effect, particular to the area, which might switch the disease on in some people."
Frances Hall, secretary of the Human BSE Foundation, also welcomed the investigation.
"These cases obviously need investigation," she said.
"Sadly, it comes too late for the people who have already died."
The Leicestershire CJD "cluster" was first reported in November 1998, after the first three deaths.
Health officials in the county have so far been operating a wait and see policy on how the disease develops.