Meanwhile, health and safety experts are working to determine whether the foot-and-mouth disease outbreak came from a high-security government laboratory or from a private pharmaceutical company on the same site.
They are also investigating whether its spread was accidental or deliberate.
Despite easing the transport ban, authorities ordered the slaughter of livestock on a third farm suspected of having the disease on Wednesday.
The farm was next to another where cases of foot-and-mouth were confirmed on Tuesday.
Reynolds said the order was a precaution and tests were under way to determine whether any more animals had been infected.
She said that the strain found on the second infected farm was identical to that found at the first outbreak, and that used in the laboratories.
Reynolds said there was a "low, but not negligible" risk of the disease spreading outside the surveillance zone set up around the lab and the affected farms.
Britain's health and safety agency said in a report late on Tuesday that there was a "strong probability" that the outbreak originated at the Pirbright laboratory site southwest of London and was spread by human movement.
The drug company being investigated as a possible source of the outbreak insisted there had been no breach of its biosecurity procedures.
The department for environment, food and rural affairs said on Wednesday that officials were investigating a vegetable plot near one of two infected farms.
Newspapers reported that they were looking into the possibility a lab worker had carried the virus to the vegetable patch on boots or clothing.
Vaccine-maker Merial Animal Health, the British arm of US-French Merial Ltd, said "intensive internal investigations" had found no evidence of breaches.
In a statement the company said: "To date, we have not been able to establish any evidence that the virus may have been transported out of our center by humans.
"We fully support the investigation and will continue to co-operate and provide complete access to our centre to enable these investigations to continue."
China and Mexico joined other countries, including the United States, in banning imports of British livestock and their products on Wednesday.