The disease is also taking its toll on sporting fixtures, with all horse-racing in England and Wales cancelled from Wednesday.
Mr Brown also revealed a £152m rescue package for beef, sheep and dairy farmers, and a scheme to allow the movement of disease-free livestock to abattoirs under licence.
The announcement came as six new cases of the disease were confirmed in the UK, bringing the total number of outbreaks to 18.
The disease is also taking its toll on sporting fixtures, with all horse-racing in England and Wales cancelled from Wednesday.
In addition, the rugby union match between Ireland and Wales in Cardiff has been cancelled due to fears that travelling supporters could carry back the infection.
And members of the Muslim community have been urged to carry out annual sacrifices - or Qurbani - for next week's Eid al Kabir festival, outside the country.
Click here to see map of confirmed cases
The Halal Food Authority made the recommendation because of the ban on the movement of animals and because the culls will lead to a shortage of animals available for slaughter.
Meanwhile the farmer at the centre of the crisis, Bobby Waugh of Heddon-on-the-Wall, Northumberland, said on Tuesday his pigs had been fed on swill made from school dinners.
Sunderland City Council is trying to establish the origin of meat served in its schools.
Nick Brown said there would be no compensation for hauliers, abattoirs and food processing firms hit by the outbreak.
Using government cash to compensate them would be in danger of infringing EU rules, he said.
"We have always taken the view that consequential losses necessarily involved in the control of animal disease are the responsibility of the industry," he said.
But he said he hoped the licensed movement of animals would help ease financial pressures on the industry.
He said: "We are doing our very best to help the industry. The best thing we can do is to extinguish the disease."
Paths closed
New emergency powers have given councils the authority to close public footpaths and rights of way as a temporary precaution.
It could mean huge swathes of the UK countryside will be out of bounds to the public.
Mr Brown said: "Our advice remains that people should take sensible precautions in the countryside, and avoid unnecessary visits on farms and especially close proximity with livestock."
People have been told to stay away from National Parks, including Exmoor.
The latest outbreak of the disease was at an abattoir in Okehampton, Devon, adding to the total of six new cases were confirmed on Tuesday.
The outbreak includes Wales for the first time, at an abattoir in Anglesey which has been under investigation for some time. The animal involved was from Yorkshire.
The other cases were confirmed at Wolsingham in County Durham, Withnell in Lancashire, Wootton in Northamptonshire and Okehampton in Devon.
Ban extended
Britain has placed an emergency ban on meat and dairy exports in a bid to stop the disease spreading.
European Union vets announced on Tuesday that they were extending this ban until 9 March.
The money for the government's compensation package will be drawn from a European Commission fund.
In addition, the government also announced that a scheme compensating pig farmers wishing to leave the industry would be extended.
There are as yet no recorded cases of foot-and-mouth in mainland Europe, but hopes the crisis could be confined to the UK have receded with the confirmation that livestock from a British exporting farm have the disease.
Several countries have already introduced emergency measures to prevent the disease emerging in their herds, with France announcing it is to destroy 20,000 sheep imported from Britain.
