The UK’s farmers face a profound crisis in the event of a no-deal Brexit, and there is dangerous ground ahead even if a deal is agreed, according to the head of the National Farmers’ Union.

Minette Batters, the union’s first female leader, is determined to be cautiously positive about Brexit, for which a majority of farmers voted. “We have to embrace the future … and make sure we have a goal and a plan,” said Batters, who declined to reveal how she voted in the referendum.

But she is extremely worried by the possibility of no deal. In that case, she said, the government had “made it clear that they would obliterate the tariff wall on food so that products could just keep coming in here without a tax – that is what they’ve said. Which makes sense, because who wants to see food prices rising?”

A government briefing in December suggested that in the event of no deal, the government could allow some products to continue to enter the UK without paying a tariff to keep food prices stable.

Batters pointed out that UK farmers would have third-party status and would face high tariffs to sell their goods into Europe. “We’d be priced out of the market,” she said, claiming that the result for UK farmers would be catastrophic. “Forty per cent of our lamb goes to Europe, for just one example. We’re not going to suddenly start eating more lamb here. If we don’t have that export market, what happens to it?”

Some experts have predicted that 25% or more of farmers could go out of business in the first year, which Batters does not think is impossible.

British food should be selling itself around the world on its high welfare standards and environmental stewardship, Batters argues, and she has laid down an ambition for UK farming to reach net zero carbon emissions by 2040. “We want to have a big British brand and going to net zero is part of that ambition … part of a much bigger joined-up plan that delivers on many fronts for society.”

Animal welfare and environmental campaigners point out the irony of these moves from the NFU, which resisted environmental and welfare reforms for years.

Batters also has reservations about Michael Gove’s plans to move UK farmers away from the EU system of subsidies based on land area and towards a “public money for public goods system”, where farmers would be paid for environmental services. The environment secretary’s agriculture bill will go to the House of Lords this month: under its terms, the current subsidy system would be phased out over seven years and the new system phased in.

Both Batters and environmental campaigners are concerned that despite trumpeting high UK standards, the government refuses to include them in the legislation. The US has said it will only do a trade deal with the UK if it accepts America’s very different food standards, and there are fears that the British government is trying to leave the door open for a possible US deal, which would have a huge impact on UK farmers.

“It would be very unfair on British farmers and consumers if they were then subjected to product coming in where they’ve had access to things that we’ve had banned in this country,” said Batters.

The shadow trade secretary, Barry Gardiner, told the Oxford Farming Conference this week: “The rhetoric has been great on standards.” But Gardiner said that during the progress of the legislation, every time Labour tried to add amendments to get the standards included, the Conservatives made sure the amendments failed.

“Liam Fox is still up for a ‘quick and massive deal’ with the US,” Gardiner said, claiming that lower food standards could be imposed under the powers the government has given itself.

Brexit is just one of a number of existential issues faced by farmers in the next 10 years. A tax is being proposed on red meat, known to be a significant contributor to climate change. Meanwhile, innovative companies around the world have been creating alternatives to milk and meat that are starting to eat up large chunks of the market. Gene editing, robotics and big data are all growing in influence, each presenting different challenges.

So are UK farmers ready for the tidal wave of change that is coming their way? “No,” said Batters. “And that’s why it’s a good thing that we have seven years to look at turning things around.”