Ministers are facing the prospect of having to abandon the controversial cull of badgers in England, for this year at least, due to fast-rising costs, the Guardian has learned.

The cull, aimed at curbing the rising infections of tuberculosis (TB) in cattle, is running out of time to begin before winter weather means the badgers lie low in their setts. The environment secretary, Owen Paterson, and farming minister David Heath cancelled a series of interviews on Thursday, but department officials said there was no U-turn: "There is no change to the badger cull policy. We want the cull to happen as soon as possible."

The Guardian can reveal that the estimated number of badgers in the pilot cull areas in Gloucestershire and Somerset have turned out to be far higher than the figures used to estimate the initial cost. Farmers must commit to killing at least 70% of the badgers in the cull zone, or fleeing badgers will spread TB further. But the Guardian can also reveal that each culled badger carries a bounty on its head, which means that having to kill more badgers means costs must rise.

In a parliamentary answer on Wednesday, Heath told shadow environment secretary, Mary Creagh: "The best estimate for the number of badgers within each pilot area is: west Gloucestershire, 3,600; west Somerset: 4,300." However, the environment department's original, generic estimates, before recent surveys were conducted, were 2,000-3,000 for cull zones of that size. The figures show killing costs have as much as doubled in the case of Somerset.

A Whitehall source told the Guardian that, because the killing costs have to be borne by farmers and landowners, the National Farmers' Union (NFU) president, Peter Kendall, feels the cull may now be too expensive to carry out, given the new higher badger numbers. The government's own impact assessment had already shown that carrying out the cull will cost more than it saves. A spokesman for the NFU said they did not recognise that view from Kendall and were not aware of any change in the government's policy.

Creagh said: "The abandoning of the cull would be good news because we have always said the cull was bad for wildlife, bad for farmers and bad for taxpayers. The science is clear that it risks making things worse." On Sunday, 32 eminent scientists, including those who designed and ran a landmark 10-year culling trial, called on ministers to halt the cull. But ministers argue that the rising costs of bovine TB – £90m in 2011 and 26,000 cattle slaughtered – means that culling has to go ahead, alongside tighter biosecurity and investment in vaccination research.

The cull licences were issued by Natural England for Gloucestershire on 17 September and for Somerset on 4 October. The companies managing the culls were then required only to complete some "administrative" steps before culling could begin, but they have not. Farmers are required to deposit enough money to fund the entire four-year cull before beginning, because failing to complete the entire cull is near certain to increase bovine TB. Natural England said not all the money had been deposited, although a spokesman added he did not think the issue was a "deal-breaker". He added that the drawing in of winter meant that "the sooner the cull started, the better."

The bounty being paid for each badger carcass was revealed to a concerned member of the public by Natural England. The bovine TB licensing unit emailed her: "When the method employed free shooting, contractors are paid per badger."

The Whitehall source said: "Everyone in the department is scrambling with increasing desperation to make an unworkable policy work, so Paterson doesn't look like the failure David Cameron and Nick Clegg saw his predecessor Caroline Spelman as being." Paterson has been holding daily meetings on the cull.

Further confusion arose on Thursday when Paterson twice cancelled a television interview with ITV News for "logistical reasons" and Heath cancelled a Friday interview with the Daily Telegraph.

The cull has prompted the largest animal rights protests since fox hunting was banned in 2004, and more than 150,000 people have signed an e-petition to stop it. The petition has granted opponents of the cull the first ever debate in the House of Commons, set for 25 October, where the government will have to vote down a motion to halt the cull.