"We are looking at weeks at least, because we have to visit farms, slaughter all the infected pigs and then clean and disinfect and check all the infected sites."
Jim Scudamore fears the ban, imposed by the three countries because of an outbreak of swine fever on farms in East Anglia, could widen to more EU countries.
He said experts would travel to Brussels within a fortnight to discuss animal and public health issues with the European Commission's scientific veterinary committee, but thousands of pigs would have to be slaughtered in the interim.
The ban was imposed after pigs at three East Anglian farms were found to have swine fever. Outbreaks have also now been confirmed at two further farms, thought to be in Suffolk and Norfolk.
Fifteen per cent of British pig production is exported, and the Meat and Livestock Commission (MLC) has warned a ban could have a "devastating effect" on the industry.
Hundreds of farms are now being checked after the first three cases of swine fever were traced to one farm in East Anglia.
The Ministry of Agriculture (MAFF) refused to reveal the exact location of any of the sites of infection, but the latest two confirmed on Saturday are both understood to be near Bungay, Suffolk.
Limiting the spread
Mr Scudamore told BBC Radio 4's Today programme: "The difficulty will be if it has spread any further.
"We are looking at weeks at least, because we have to visit farms, slaughter all the infected pigs and then clean and disinfect and check all the infected sites."
He admitted the outbreak could have a "major impact on the pig-farming industry".
Several EU countries have suffered serious outbreaks of swine fever over the last five years, and they are "extremely sensitive" about the disease, said Mr Scudamore.
'Devastating effect'
EU states, he said, are free to impose interim embargoes on imports while awaiting a meeting of the veterinary committee in Brussels.
Chris Luckhurst, of the MLC, also voiced his concerns about the impact on the UK's pig farming industry.
"If we are seeing bans from European countries, we will have to refer it to the commission because it will have a devastating effect on the industry," he said.
"Most pig farmers have been making quite large losses for the last two years and they really are not in a financial situation to be able to bear any additional losses at the moment."