A mass cull of cattle, not badgers, is the only large-scale action that can end the scourge of tuberculosis in England’s livestock, according to new scientific research that represents a heavy blow to the government’s current policy.

The work is the first national-scale model of how the disease spreads and also found that more rigorous cattle testing and cattle vaccination would significantly curb the disease. But it concluded that the impact of the government’s favoured option of a widespread badger cull would fail to prevent the epidemic growing.

The research was published on Wednesday in Nature, one of the world’s most prestigious scientific journals, and is a heavy blow to environment secretary Owen Paterson and his ministers, who have resolutely backed the badger cull as an essential part of tackling the disease. The study was immediately rejected by farming minister George Eustice, who said a mass cull of cattle would kill the industry.

TB in cattle has soared in recent years and over 26,000 cattle were slaughtered in 2013 at a cost to taxpayers of £100m. Many scientists have dismissed the badger cull as an expensive and potentially dangerous distraction and the pilot culls in 2013 were judged not to be effective of humane by an independent panel.

The one-off cull of all cattle in infected herds which is considered in the new paper would see over 250,000 animals slaughtered, about 20 times the current annual rate, though far fewer than the 6.2 million animals killed in the 2001 foot and mouth epidemic. Prof Matt Keeling, an epidemiologist at the University of Warwick and one of the research team, acknowledged the measure would be “draconian” and “unpopular” but said that, because the cattle cull would cut TB infections, far fewer cattle would be slaughtered in following years. “This might be an acceptable cost if one is prepared to take a sufficiently long term view,” the team write in the paper.

The effectiveness of whole-herd culling stems from it tackling several key routes of infection at once: infection spreading within herds, infected animals failing to be detected by the current imperfect test and from fields harbouring infected manure.

The new model is based on the detailed data on the daily movements of cattle within the entire national herd and it replicated reality closely when tested. The model incorporates all the mechanisms of TB transmission, but lack of data meant badger-to-cattle transmission was not explicitly included, though was bundled with infection from other environmental sources such as manure, droppings and other wildlife. Slashing this environmental route of infection by 50%, mimicking a huge badger cull, led only to a curbing of the annual increase in infections from 10% to 6%.

Keeling said: “We are not advocating a whole-herd cull, but we are putting it up there. We wanted to ask if you went all out to combat it, what could you possibly do.” He added that the team’s “dispassionate analysis” showed the arrival of infected cattle was responsible for the vast majority of newly infected farms, rather than local environmental factors such as TB-carrying badgers.

Facebook Twitter Pinterest Badgers walk past curious cattle on UK farm Photograph: Jason Venus/Alamy

Robbie MacDonald from the University of Exeter and not part of the research team, said the work was groundbreaking: “The model is unprecedented in its scale, realism and approach.” He said the suggestion of a one-off mass cull would be “horrifying” for ministers, farmers and animal welfare campaigners, but that the work raised the question of whether the continued slaughter of tens of thousands of cattle for many decades was a worse prospect. He said the model showed cutting transmission from the environment, such as badgers, “is likely to yield unimpressive results and contribute little biologically to controlling a national epidemic”.

“This finding is important given the massive cost, effort and controversy associated with badger culling,” said Prof Rosie Woodroffe, an expert at the Institute of Zoology and part of the team that carried out a landmark decade-long trial of badger culling. Woodroffe, who has recommended vaccination over culling to reduce TB in badgers, said: “This paper predicts that controlling TB in the short and medium term would be more effectively achieved by management targeted at cattle.”

But Eustice, the minister with responsibility for the cull, said: “We cannot accept the paper’s findings because it does not investigate the full range of ways in which TB could spread. What this paper proposes would finish off the cattle and dairy industry in this country. TB is devastating for our dairy and cattle farmers and, along with blanket testing and removal of infected cattle, biosecurity measures, vaccination and cattle movement controls, [badger] culls will help get this disease under control.”

Lord John Krebs, professor of zoology at the University of Oxford and who commissioned the landmark badger culling trial, said: “The sophisticated model and conclusions described in this paper give further support to the view that culling badgers is not an effective strategy for controlling bovine TB. It is to be hoped that Defra takes on board this latest piece of scientific evidence.”

Dominic Dyer, CEO of the Badger Trust which is currently challenging the badger cull in the high court, said: “This groundbreaking report should be the final nail in the coffin of the disastrous badger cull policy. This report clearly shows that the most effective way to reduce bovine TB is not to kill hundreds of thousands of badgers. Calling an immediate halt to all future badger culls will deliver a good result in the battle to eradicate this disease not only for farmers, but also for taxpayers and our precious wildlife.”

Since 2013, ministers have tightened restrictions on the movement of infected cattle and increased testing but, despite recent falls in bovine TB, Keeling said it was too early to assess the impacts of the policy changes. He emphasised the complexity of tackling the TB epidemic in cattle: “It is a difficult disease to control. The only things we can see to control this disease are extreme measures.”