UK ministers are expected to offer Australia a trade deal which will gradually eliminate all tariffs and quotas, one seen as a victory for free-trade Brexiters in the cabinet but likely to prompt alarm among UK farmers.

Downing Street did not deny reports on Friday that the likely offer to Australia would be a transition to zero quotas and tariffs over 15 years, although insisted discussions were still taking place.

Such an outcome would be viewed as Boris Johnson siding with Liz Truss, the international trade secretary, against the views of the environment secretary, George Eustice, who is understood to be worried that large-scale Australian beef and lamb producers could undercut UK farmers.

With a deal informally scheduled to be agreed next month, on Thursday Johnson chaired a meeting of ministers, including Truss and Eustice. According to the Sun and the BBC, the eventual decision was to seek a 15-year timetable to zero tariffs and quotas.

The National Farmers’ Union has warned that a series of post-Brexit trade deals which offer full access to the UK market to producers in other countries could cause “irreversible damage” to UK farming. Ministers have promised to protect domestic farmers, but have not said how.

Asked about this during a broadcast round on Friday, the justice secretary, Robert Buckland, said any deals would “of course take into account the very high welfare standards we apply here in the UK and will of course make sure British farming and British farmers are not undercut, are not put at a disadvantage, bearing in mind the quality and excellence of the products which are made here in the UK”.

He told BBC Radio 4’s Today programme: “That is at the heart of our trade policy and that will be adhered to in respect to both Australia and indeed other trade deals that will be looming over the horizon in the months and years ahead.”

The projected Australia deal is seen as totemic for the government, as it would be the first new deal made after Brexit, rather than a rolling-over of those formerly made as part of the EU. However, its terms could upset Tory MPs in rural constituencies, as well as other government allies.

On Friday Edwin Poots, the leader of the Democratic Unionist party, who is agriculture minister in Northern Ireland’s devolved administration, wrote to Eustice to express his opposition to a zero-tariff, zero-quota deal with Australia.

“The prospect of such a deal presents a high level of risk to Northern Ireland and UK farmers,” he said. “Therefore I believe that the UK should maintain tariff protection at present levels for all agricultural products where the UK has a significant production interest.”

Johnson’s spokesperson said the prime minister “wants to maximise the massive opportunities presented by post-Brexit trade deals”, but UK farmers would be protected.

He said: “There are a regular series of meetings on not just this trade deal but the deals we have been working on throughout.”

Meanwhile, Australia’s trade minister, Dan Tehan, has talked up the chances of a swift agreement, saying recent talks with Truss had been productive.

“By the end of it, we built such momentum, then we decided, well, why don’t we go for the sprint for the finish line,” he told an Australia-British chamber of commerce event on Friday.

Tehan said both sides had made an agreement not to get into any of the finer details until the deal was done, but said he was confident any concerns UK farmers had could be mollified.

“What I would say to UK farmers is that the Australian agricultural industry and the UK can work together, I think, to enhance agricultural production in the UK and enhance agricultural production here in Australia,” he said.