Downing Street has said the prime minister remains opposed to any form of referendum being attached to a Brexit deal, as the government prepares to enter its seventh week of talks with Labour to find a compromise.

The shadow Brexit secretary, Keir Starmer, and the deputy Labour leader, Tom Watson, have said a deal is unlikely to pass without a referendum as part of the package, with up to 150 of the party’s MPs prepared to vote against an agreement without one.

Key figures from both sides including Starmer, John McDonnell and Rebecca Long-Bailey, as well as the chancellor, Philip Hammond, Theresa May’s de facto deputy, David Lidington, and the environment secretary, Michael Gove, are set to meet again on Monday afternoon.

Downing Street said May had made clear her views about a second public vote: “She has said on many occasions that she is focused on delivering the result of the first referendum.”

May’s spokesman declined to put a deadline on the talks but said the government was prepared to move on to a series of indicative votes in parliament if no resolution was possible.

“If we were able to make progress with Labour then we would look to bring the bill before the House of Commons before the European elections,” he said.

Both Labour and government sources have suggested the two sides will need to take stock on the likely progress of the talks this week, and the effectiveness of continuing discussions is likely to be discussed at cabinet on Tuesday morning.

In an interview with the Guardian, Starmer said they could not expend much more time simply exploring each others’ positions.

“Is the government actually prepared to change its red lines? The answer is, so far, not really,” he said. “On substance, there is a considerable distance between us.”

“I think it would be wrong in principle to use up much more time simply exploring each other’s positions,” he said. “I do think we do probably in the coming days need to make that assessment.”

On Monday, two cabinet ministers made clear their opposition to including a fresh poll. The housing secretary, James Brokenshire, said a confirmatory referendum would be “taking us in a different direction, that’s actually saying: ‘Well, we’re looking at this issue all over again and not giving effect to the original vote.”’

However, he described the cross-party talks as “very serious”, adding that if it were not so, “we wouldn’t have committed all of the time and effort on all sides in relation to this.”

The foreign secretary, Jeremy Hunt, said he remained optimistic the talks could make progress, but said a referendum would a “betrayal of what people voted for” in 2016.

“We are talking to the Labour leadership, we have had very detailed discussions,” he said. “People have been pessimistic that these discussions won’t go anywhere but they have continued, this is a crunch week.”

The DUP leader, Arlene Foster, whose party is in a confidence and supply agreement with the government, said a confirmatory Brexit referendum would place democracy at risk.

Foster, who was attending the launch of her party’s European election manifesto in Belfast, said May had no vision for the post-Brexit future of the UK.

“What people want to see is democracy being respected. Unfortunately it hasn’t been respected and we have a remain parliament, therefore parliament has not been able to deliver on Brexit in the way it should have been delivered upon,” she said.

“We have a prime minister, frankly, who doesn’t have the vision for the United Kingdom post-Brexit that we all want to see. We want to see a United Kingdom that is strong post-Brexit and has a close relationship with Europe.”