The Democratic Unionist leader, Arlene Foster, has said she and her 10 MPs will not vote for a second EU referendum but did not rule out backing a “Norway-plus option” that is gaining support in the Commons.

In an interview on BBC Radio 4’s Today programme, Foster confirmed the DUP’s opposition on Theresa May’s withdrawal deal over the proposed backstop arrangement for Northern Ireland.

She urged the government to look for a better deal that did not treat Northern Ireland differently. Foster said: “If the backstop is implemented, there will be checks between Great Britain and Northern Ireland … and that means there will be extra costs for the people of Northern Ireland.”

Quick guide What is the common market 2.0/Norway-plus Brexit option? Show Hide This soft Brexit compromise has been championed as a plan B for leaving the European Union. It is based on Norway’s relationship with the EU, which is outside the bloc and the customs union but inside the single market. Under the plan the UK would have to join Norway, Liechtenstein and Iceland in the European Free Trade Association (Efta), which would then allow it to participate in the European Economic Area (EEA). The ‘plus’ in this option refers to a temporary customs union with the EU, which would need to be negotiated to avoid a hard border on the island of Ireland. This arrangement would remain in place until the EU and UK agreed a specific trade deal. The option has the advantage of being as close to the EU as possible without full membership, and it would do away with the need for the problematic backstop for Northern Ireland. Like Norway, the UK would be outside the common fisheries and agriculture policies, and would not be subject to the European court of justice. But it crosses a key red line for Brexiters by continuing freedom of movement, one of the preconditions of single market membership. It would also limit the UK's ability to negotiate its own trade deals while a new customs arrangement is under discussion. And it would require continued financial contributions to the EU without an influence, as the UK would no longer have MEPs or a seat on the European Council. It also isn't entirely clear that the UK would be welcomed into Efta.

Foster said the separate treatment of Northern Ireland under the withdrawal agreement was “not a slight difference”. “I think it is 291 regulations from Europe that we have absolutely no say in after we leave the European Union,” she said. “There is a huge democratic deficit coming our way if we agree to this deal, because we have no say over the rules that will apply to Northern Ireland.”

Asked about a second referendum if May’s deal was rejected in parliament, Foster said: “We won’t vote for another referendum.”

She appeared more open to a Norway-plus compromise in which the UK would join the European Economic Area. Proponents of the option point out it would avoid a hard border with Northern Ireland because the UK would stay in a customs union with the EU.

Asked about the idea, Foster said: “We have always been very clear with the government that our one red line was that we shouldn’t be differentiated from the rest of the United Kingdom in terms of customs and in terms of regulatory alignment.

“We are very open to allow the government to work away at other solutions in terms of what is the best way to leave the European Union.”

But she stopped short of fully signing up to the Norway idea. “What we are saying is let us not waste time on this deal where there is no enthusiasm – and it is very clear to me that it is not going to get support in the House of Commons.

“Let us look for a better deal. A deal that is good not just for Great Britain, but is good for Northern Ireland as well. What we want to see is taking back control of our money, and our borders and our laws. And unfortunately Theresa May’s deal doesn’t do any of that.”

Asked if the Norway option might do that, she said: “No I’m not saying that. I’m saying that we should look for a better deal. And we of course are speaking to colleagues in the Conservative party and indeed wider right across Westminster to try to find that better deal. We are not going to be prescriptive in that better deal. What we want to do is to make sure that the referendum result is respected.”

Elsewhere, the prime minister’s deal gained the backing of Andrea Leadsom, the Commons leader and a prominent Brexiter, who had appeared ready to resign from the cabinet over the agreement.

Leadsom was one of the “pizza club” of pro-leave Cabinet ministers who held informal meetings to discuss their response to May’s plans. But in a letter to her constituents she said the withdrawal agreement should be backed as “there is no other deal on the table”. She admitted that endorsement came after a “challenging journey”.