And the Environment Secretary Hilary Benn has in the past also said that public acceptance would be a factor in determining the government's policy.
But Sir David said while he did not want to see badgers killed, the problem remained unresolved.
"In some areas the instance of TB in badgers is very high indeed and there is no policy at the moment for managing TB in badgers, and as long as that continues I'm afraid the epidemic will inexorably continue to spread across the country."
However, the decision was welcomed by prominent scientist Lord Krebs, who designed the experiments on the effectiveness of badger culling for the ISG.
"If this report [on the government's decision] is true then Hilary Benn has made the right decision," he said.
The ISG's analysis showed that sustained culling over a large area for five or six years might have some effect, "but even that is not clear-cut", according to Lord Krebs.
He said: "It's not practical to carry out that kind of scorched-earth cull over a prolonged period for a policy that may not even work."
According to Lord Krebs, the incidence of TB in cattle is increasing very slowly, and he believes that the disease could be brought under control through better surveillance and biosecurity.
Badger groups have fought a campaign against a mass cull.
Trevor Lawson, from the Badger Trust, said rejecting the idea of a badger cull would be the "right decision, based on sound science, which will allow farmers to move forwards in tackling this disease".
"There is no scientific, economic or practical case for culling badgers to control bovine TB," he said, adding that attention should be focused on cattle as "the main agents of the disease".
But the NFU's Mr Kendall said the disease was spreading at an "incredible" rate and needed to be dealt with.
"This is wiping out big chunks of UK farming and is ruining farming families and the rural economy. We need to take tough decisions. It's never popular but the farming industry will be devastated."
He added that the government was failing to show leadership.
"If we can't make difficult, disease-related decisions, based on science, we are in a mess," he said.
In May, a report by badger groups claimed the "virtual extermination" of badgers in the Republic of Ireland had failed to stop the spread of bovine TB.
But the NFU accused the groups of being selective in their use of figures and argued that controlled, selective culling of wildlife around infected farms in the Republic had brought considerable success in reducing the incidence of the disease.
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