Nicola Sturgeon is expected to lead a historic shift in the Scottish National party's approach to devolution by championing home rule within the UK in a bid to challenge Labour's power bases in central Scotland.

Sturgeon, now deputy first minister, is on the brink of being confirmed as Alex Salmond's successor as SNP leader and first minister this week after unanimous endorsements from senior colleagues.

After the party lost the independence referendum last Thursday by 2m votes to 1.6m, senior figures within the SNP believe Sturgeon will reverse Salmond's long-held strategy of refusing to cooperate on devolution by instead making detailed proposals for new powers. Such a move would sharply differentiate Sturgeon's tactics from those of her mentor, Salmond.

Under Salmond's two terms as party leader, the SNP refused to take part in the coalition of parties and civic groups that pressed for the new Scottish parliament to be set up in the 1990s. As first minister, he refused to work with the Calman commission set up by the UK parties in 2008 to give Holyrood new income tax powers coming into force in 2016.

Mike Russell, the Scottish education secretary, said that would allow Sturgeon to "hold their feet to the fire" by going for maximum devolution of tax and welfare powers – a policy known as home rule within the UK.

That would go far further than the current offer from the UK parties of controlling just income tax and housing benefit, and allow the SNP to get far closer to their goal of independence.

That would then allow the SNP to tell Labour supporters who voted no last Thursday on the grounds that the UK parties had guaranteed extra powers for Holyrood that they are the champions of real devolution to Scotland.

With 10,000 people said to have joined the SNP in the last two days, that in turn would be the springboard for an SNP challenge in key Labour seats at Westminster, particularly in Glasgow, North Lanarkshire and Dundee – the few places where the yes vote won on Thursday, SNP figures said.

She is expected to confirm her candidacy when nominations to succeed Samond open mid-week, after stating on Friday she could think of "no greater privilege" than to become party leader and first minister.

Salmond, clearly exhausted by the pace and intensity of the referendum campaign, announced he was to step down on Friday afternoon, eight hours after conceding defeat.

The most serious potential challengers, including Mike Russell, the Scottish education secretary and former party chief executive, and Alex Neil, Scottish health secretary and a former leadership contender, backed Sturgeon over the weekend.

With seven senior cabinet ministers now endorsing Sturgeon and none objecting, Russell told the Guardian Sturgeon was unequivocally the strongest and most popular candidate: "I'm absolutely certain she's the best candidate; I can't conceive of another one better qualified or more experienced, or more trusted by the party."

Salmond increased the pressure on Westminster to honour a late pledge to rush through new powers, after a dispute emerged between David Cameron and Ed Miliband over the full package of reforms, claiming they had been "tricked" into voting no.

"I think that their vow was cooked up in desperation from the last days of the campaign," Salmond said. "It's the people who were persuaded to vote no who were misled, who were gulled, who were tricked effectively. They are the ones who are really angry."

Downing Street and Miliband denied that, despite deep differences over Cameron's plan to link more devolution with restrictions on Scottish MPs' voting rights at Westminster. Number 10 said it had "made clear commitments on further powers", while Miliband said the timetable would be honoured, "no ifs, no buts".

The SNP said its membership had leapt by more than a third, from 26,000 to 36,000 in the days after the referendum, with the Scottish Green party disclosing it had 2,000 new members and the Scottish Socialist party 1,000 new members.

Senior figures believe the SNP should seek another coalition to fight the election with the Greens and SSP, both of which were junior partners of the pro-independence umbrella campaign Yes Scotland, to exploit any failure by the UK parties to offer significant extra powers.

Ian Blackford, a former SNP Treasury, said increasing the number of SNP MPs in the Commons from the current six would give the party a clear popular mandate to demand far greater devolution.

The SNP should ask voters to "lend us your support at the election, because the SNP is the best and only vehicle to deliver that change," he said.

Russell and other senior figures stated on Sunday that the SNP should accept an offer by the UK parties to collaborate on their offer of more powers for Holyrood.

With some yes campaigners, such as the artists' group National Collective, insisting that the independence campaign should continue, Russell said the country should accept the yes campaign lost on Friday and focus instead on maximising devolution.

Their failure to do so after working with the SNP would strengthen the party's case for full independence. "The proof has to be seen as to whether these powers can be delivered by the union," he said.

"I don't think there's any debate at all on the type of society we want in Scotland. This is a moment to hold Westminster's feet to the fire and see whether it can be done that way."