Figures released on Monday show officials expect agriculture and other food related sectors to take a roughly £150 million hit from the new agreement.
The official impact assessment describes the change sparked by the deal as a "reallocation of resources within the economy" and a "process of economic adjustment".
Ministers were accused of "selling British farmers down the river" but the trade secretary Anne-Marie Trevelyan said the deal, signed today, "will slash red tape".
The agreement will result in the scrapping of tariffs on many agricultural products coming from New Zealand and UK farmers have said it could drive them out of business.
The deal is overall not expected to have a significant impact on the UK economy, with an expected gain of between just 0.02 per cent and 0.03 per cent by 2035 – a total of around £12 per person by that date.
But officials admit it could have sharper more concentrated effects on certain sectors of the economy – some negative.
"The economic benefits of FTAs do not arise without reallocation of resources within the economy (sometimes referred to as the gains from greater specialisation)," the newly revised impact assessment says.
"The process of economic adjustment gives rise to adjustment costs for affected sectors, businesses, and their employees.
"The overall structure of the UK economy remains broadly unchanged by the agreement.
"However, part of the gains results from a reallocation of resources away from agriculture, forestry, and fishing (around -£48 million) and semi- processed foods (around -£97 million)."
Farmers have previously warned of “huge downsides” to the deal, with the National Farmers Union (NFU) saying it “could damage the viability of many British farms in the years ahead”.
Some concerns about the deal are related the whether UK farmers will face unfair competition because they have to enforce higher production standards than those abroad.
Katie White, campaigns chief at the environmental charity WWF, said on Monday that the new free trade agreement "opens the door to food produced in ways that harm nature and fuel the climate crisis, undermining the UK’s own transition to more sustainable farming".
She said the UK should "adopt a set of core standards – including environmental standards – set in UK law, which will allow us to open up trade in the best products from around the world, but ensure we can filter out goods that are produced at high environmental cost".
Responding to Monday's news, NFU president Minette Batters said there would ultimately "be no limit to the amount of goods New Zealand can export to the UK".
She added: “I have consistently pointed out that the real risk to UK farmers, and longer term for people wanting to buy British food, from the government’s approach to trade deals is not the individual deals themselves but the cumulative impact of each deal when added together. This deal today shows I was right to be concerned.
“Once again, there appears to be extremely little in this New Zealand trade deal to benefit British farmers. UK farm businesses face significantly higher costs of production than farmers in New Zealand, and margins are likely to tighten further in the face of rising input costs, higher energy bills and labour shortages.
"The government is now asking British farmers to go toe-to-toe with some of the most export-orientated farmers in the world, without the serious, long-term and properly funded investment in UK agriculture that can enable us to do so; the sort of strategic investment in farming and exports that the New Zealand government has made in recent decades."
Mark Tufnell, president of the Country Land & Business Association (CLA) said there was clearly "opportunity for New Zealand farmers in this deal" but that it was less clear "what the opportunity is for those of us in the UK".
He added: “Over time, New Zealand will be able to sell even larger quantities of meat and dairy produce into the UK, often produced much more cheaply than we can do ourselves. This risks undercutting UK farmers and putting a question mark over the viability of their businesses.
“Government is leaving the industry in the dark about what this deal really means for agriculture, setting a worrying precedent for other Free Trade Agreements we may strike with other major food exporters – many of which have far lower animal welfare and environmental standards than we do.
"Government promised that suitable checks and balances would be put in place to ensure we would not be undercut in this way. So far they have failed to materialise."
Ministers are however keen to sign trade deals abroad in order to highlight the supposed benefits of leaving the European Union.
Liberal Democrat Trade Spokesperson Sarah Olney said: "The Government has negotiated a trade agreement that will actively damage the UK's farming communities and will bring next to no tangible benefits to our economy.
"The Conservatives have proven that they are utterly unable to negotiate trade deals that boost the UK economy and unfortunately this agreement is no exception.
"The economic benefits are a drop in the ocean and they will do nothing to mitigate the damage from the red tape and paperwork caused by Boris Johnson's shambolic EU trade deal.
"Instead of delivering Global Britain, this Government is selling British farmers down the river."
The government’s publicity around the deal has focused on potential benefits to other parts of the economy, such as the services sector.
Announcing the deal, international trade secretary Anne-Marie Trevelyan said: “This deal will slash red tape, remove all tariffs and make it easier for our services companies to set up and prosper in New Zealand.
“Our trade with New Zealand will soar, benefiting businesses and consumers throughout the UK and helping level up the whole country.
“Like all our new trade deals, it is part of a plan to build a network of trade alliances with the most dynamic parts of the world economy, so we set the UK on a path to future prosperity.”
A spokesperson for the Department for International Trade said: “British food and drink are among the best in the world. Our deal with New Zealand will be fair and balanced and in the best interests of the whole of the country.
“It includes protections for the agriculture industry and tariff liberalisation for sensitive goods will be staged over time, giving UK farmers time to adjust.
“A deal with New Zealand is also a stepping stone to joining the £8.4 trillion CPTPP trade bloc, where demand for British beef is increasing, and will mean more opportunities for British exports to those high growth markets.”
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