Nicola Sturgeon hopes the Scottish National party can help engineer a political crisis at Westminster that will force MPs to reconsider continued UK membership of the EU single market and customs union after Brexit.

The first minister used a television interview on the eve of her address to the party’s annual conference in Glasgow to say its 35 MPs would almost certainly refuse to support any divorce deal obtained by Theresa May in November.

She said that if there was no Commons majority in favour of the form of Brexit envisaged by the Tory leadership, it would mean “everything is to play for” and could resurrect hopes of a Norway-style deal with Brussels.

Sturgeon believes withholding support would make it impossible for the UK government to build a majority in favour of a hard Brexit and would create a position that could attract pro-European MPs from Labour and the Tories.

She told ITV News: “I cannot envisage us voting for anything that doesn’t include single market and customs union. [If May] brought back a bad deal, a no-deal or a blind-deal Brexit and the House of Commons doesn’t support that, then I think everything is to play for in terms of putting the single market and customs union back on the table.”

The SNP’s 35 MPs are the third largest party group at Westminster and could be crucial in the event of any tight Brexit votes. With some Conservatives likely to rebel against any deal based on May’s Chequers proposals and Labour threatening to vote against, the prime minister’s prospects of winning parliamentary support already look tricky.

The SNP’s Westminster leader, Ian Blackford, reinforced Sturgeon’s argument on Monday when he said the party would cause “maximum disruption to this Tory government’s agenda” if it continued to ignore Scotland’s objections to Brexit.

Addressing delegates at the SNP conference in Glasgow, Blackford said: “The only deal we will accept is one that keeps Scotland in the single market or customs union. Any other deal sells us short. I put the prime minister on notice we will not support any measure that threatens Scottish jobs and living standards.”

Blackford said Brexit would cause lasting harm and threaten living standards across the UK. “We will not follow the Tories through any lobby [vote in the Commons] that leads to economic destruction for citizens across Scotland and the rest of the UK,” he said.

“We will not be complicit in a blind or a no-deal Brexit. Friends, when the time comes to vote on a Brexit deal, the only deal we will accept is one that keeps Scotland in the single market and the customs union. Any other deal sells us short.”

The ultimatum raises the unlikely prospect of the SNP’s MPs walking through the same division lobbies in the Commons as Brexit hardliners including Jacob Rees-Mogg and Boris Johnson, who have said they would reject any deal that they believe would give the EU long-term power over the UK after Brexit.

No 10 said it regarded Sturgeon’s intervention as unhelpful. May’s official spokesman said: “Now is the time for the UK to be pulling together to get the right deal in our negotiations.”

Sturgeon and Blackford have also backed the alternative route of staging a second EU referendum, in which the question would be to accept the deal or remain in the union – although it is not clear that the idea could command a majority in parliament. The Labour leader, Jeremy Corbyn, has only said the option would be on the table if he could not force a general election.

SNP leaders doubt a second referendum vote will take place, but they have decided they cannot be seen to obstruct or dismiss the proposal, even it remains hypothetical.

Despite announcing on Sunday that the SNP would back a second Brexit vote without requiring preconditions, such as a pledge to give Scotland a fresh referendum on independence, Sturgeon said she was not an enthusiastic supporter of the people’s vote option.

She said the best defence against Scotland being forced to accept policies from Westminster that it had not voted for was by leaving the UK entirely. “Yes, we can look at options that might protect Scotland’s position, but fundamentally the only real protection for Scotland against having decisions imposed on us against our will is for Scotland to become independent,” she told the BBC.

In her speech to SNP delegates on Tuesday, Sturgeon is also expected to say that independence is the best guarantee that Scotland has to protect its interests while the UK government stumbles from disaster to disaster.

“It’s hard to watch that unfolding calamity and feel anything other than despair. So it is up to us – now more than ever – to offer optimism and hope,” she said in advance extracts of her speech. “Just think how much more hope will be possible when we take Scotland’s future into Scotland’s hands and become an independent country.

“An independent Scotland, just as Scotland is now, will be a beacon for progressive values – equality, opportunity, diversity and fairness. Indeed those values feel more important today than ever before in my lifetime.”

The latest opinion polls, particularly a Survation poll commissioned by the SNP, suggest a no-deal Brexit could produce a narrow majority in support of Scottish independence, although a majority currently support remaining in the UK.

Support for independence while the UK remains in the EU has hovered at around 46-47%, excluding don’t knows, for months. The SNP poll found support for independence if there was a hard Brexit had risen to 52%.