A senior Democratic Unionist party figure has ruled out backing Theresa May’s Brexit deal despite party members meeting the prime minister on Thursday.

Sammy Wilson, the Brexit spokesman for the Northern Irish party, said there was not any way in which his party could support the prime minister’s agreement.

His comments came after the DUP deputy leader, Nigel Dodds, said his party’s opposition to Irish border backstop proposals had not lessened after a meeting with May on Thursday.

Wilson told BBC Radio 4’s Today programme: “It’s not just because of the regulations which Northern Ireland would be subject to with the backstop, but also the fact we would have to treat the rest of the United Kingdom as a third country, we would not participate in any trade deals which the United Kingdom may enter into in the future and we would find that there would be a border down the Irish Sea which would impede trade with our biggest trading partner, namely GB.”

Wilson, whose party props up May’s government in Westminster, said people in Northern Ireland should be “totally relaxed” about a no-deal Brexit.

This week the environment secretary, Michael Gove, said farmers and food producers could face “considerable turbulence” if the UK left the EU without an arrangement in place. He told the Oxford Farming Conference it was a “grim and inescapable fact” there would be tariffs on exports and new sanitary and other border checks.

Wilson said: “If anyone should be worried about tariffs on beef and sheep it should be the Irish. The UK are net importers of food … It would be farmers in the EU who would find selves cut off from the main market in GB.

He said Northern Ireland farmers and businesses should be “totally relaxed” by the prospect of a no-deal Brexit. “They should be more worried about this deal because this deal is going to keep them tied to EU regulations, it’s going to cut them off from the GB market, where we send 60% of our exports, and it’s going to stop us participating in UK trade deals in the future.”

He said the Irish government were preparing for a no-deal scenario where there would be no arrangements at all with the UK and the EU, and there was no mention of what would happen along the border and what hard infrastructure would be in place.

“It was a con trick all along,” Wilson said, referring to the backstop issue, the fallback plan to prevent the return of a hard border on the island of Ireland.

The Guardian revealed this week that almost 1,000 police officers from England and Scotland are to begin training for deployment in Northern Ireland in case of disorder from a no-deal Brexit.

The plans were put in place after Police Service of Northern Ireland chiefs asked for reinforcements to deal with any trouble arising from a hard border. The training is expected to begin this month.

There has been growing concern about a no-deal Brexit. May’s attempts to woo the DUP were rejected after two days of intense negotiations. Sources suggested the meetings with the prime minister and the Conservative chief whip, Julian Smith, were “Groundhog Days” for those present. There are also no further meetings planned between May and the DUP to discuss the backstop.