Similarly, the number of animals awaiting slaughter in the county is now close to zero, falling from 89,000.
The first case of the disease on Teesside has been confirmed at a farm in Cowpen Bewley, near Billingham.
However Leicestershire and Northamptonshire have both been declared free of the virus and the government's chief scientist, Professor David King, says the epidemic has been brought "fully under control".
But farmers have warned the government to be very careful about making claims that the worst of the outbreak is over.
"We could find ourselves back in the in the previous situation. This happened in the 1967 outbreak."
But speaking to BBC Radio 4's Today programme, Defence Secretary Geoff Hoon stood by the government's statement.
"The evidence is that we are getting this very firmly under control," he said.
Misleading figures
Maff figures show the number of new cases is declining steadily and the army in Cumbria is claiming to have got on top of efforts to dispose of slaughtered animals.
Downing Street said new statistics suggested that the backlogs of animals awaiting slaughter and disposal were significantly smaller than previously reported.
It says figures suggesting huge backlogs have been misleading because of a time-lag in collecting information from local Maff offices.
More efficient methods of tracking the disease, to ensure that the figures more accurate, show that in Cumbria the number of carcasses awaiting disposal has fallen from a high of 200,000 to near 10,000.
Similarly, the number of animals awaiting slaughter in the county is now close to zero, falling from 89,000.
In Scotland and the North East, there is no discernible disposal backlog, while in Worcestershire it is said to be small and reducing.
In Wales, the disposal backlog is down from 30,000 to about 4,000, and the slaughter backlog is down to 10,000 from 90,000.
But there are still individual reports of delays and inefficiency, and the slowing of the epidemic varies widely in different areas.
For the first time, the government has been able to declare previously infected areas, in Leicestershire and Northamptonshire, officially disease-free.
But those counties had suffered a total of only four cases and it is likely to be several months before the worst-affected regions will get the all-clear.
Huge cost to economy
Prof King also said the government's policy of culling infected livestock within 24 hours and animals on neighbouring farms within 48 hours was working.
At the end March the average daily total was 43 cases a day. This had fallen to 27 by last Sunday, Prof King said.
Even in Cumbria, the worst affected area, figures were better than expected, he said.
But as the disease is said to be under control, the Institute of Directors has calculated that it has already cost the economy £20bn.
And it warns that figure could double if - as many leading farmers and vets predict - the epidemic lasts far beyond July.
Meanwhile the vaccination debate continues to rage on, with farmers' leaders arguing that it would destroy public confidence in meat and drive members out of business.
But food experts will be told at a conference on Friday that meat from vaccinated animals is safe to eat.
The Soil Association, which represents organic farmers, is urging the government to adopt this view.
A row has also broken out over plans for a mass grave to dispose of animal carcasses in Petrockstow, Devon.
Residents have safety concerns about the grave and are meeting with government officials on Friday evening to argue their case.