SNP leader challenges Ed Miliband to make it clear he will join forces after the election if the two parties combined have more seats than the Conservatives

Nicola Sturgeon has issued a direct challenge to Ed Miliband to pledge that Labour will join forces with the SNP after the general election to lock the Conservatives out of power.

In a muscular speech that positioned the SNP firmly in traditional Labour territory on the House of Lords, the NHS and the minimum wage, the SNP leader reiterated her commitment not to put the Tories into government should the nationalists hold the balance of power after 7 May, as is widely predicted.



“I call on Labour today to match that pledge, to make clear that if Labour and the SNP combined have more seats than the Tories, they will join forces with us in a vote of confidence to lock David Cameron out of Downing Street.”



Speaking to a rapturous audience of some 3,000 delegates in Glasgow, many of whom had queued for two hours to hear her, she said: “If Labour fails to make that commitment, the only conclusion people will draw is that Labour would rather have the Tories back in power than work with the SNP. And that will be the final nail in the coffin of Scottish Labour.”



Turning one of Scottish Labour’s key doorstep messages on its head, she said: “A vote for the SNP is a vote to keep the Tories out.”



Referencing the last Labour government’s policy record on tuition fees, NHS privatisation and the Iraq war, she added: “If you want a Labour government to have backbone and guts, you need to elect SNP MPs to provide it for them.”



“If you want a Labour government that won’t just be a carbon copy of the Tories but will instead deliver the real change Scotland needs, then you must elect SNP MPs to force Labour’s hand and keep them honest.”



Taking on some of Labour’s touchstone policy commitments, Sturgeon pledged that a team of SNP MPs would vote at Westminster to halt NHS privatisation in England, take action to end zero-hours contracts and to back an increase of £2 an hour in the minimum wage, taking it to £8.70 by 2020. She also called for the abolition of the House of Lords, saying that it had “no place in a democratic society”.



Admitting that recent polls, which have consistently predicted a SNP landslide at the expense of Scottish Labour, have made for pleasant reading, and that some “have given me altitude sickness”, she warned delegates to take nothing for granted.



“We must work harder over these next 40 days than we have ever done before. No let up, no resting on our laurels, no slowing down to savour the polls.



“Let me make this clear, hard graft, humility and a daily determination to earn the trust of the people of Scotland – these will be the hallmarks of our campaign.”



In a sign of the confidence running through the conference hall, and the party, she added: “No constituency is off limits for the SNP in this election. We will fight for every vote and every seat.”

Ahead of Sturgeon’s speech, Gordon Brown, the former prime minister, warned voters not to be tricked by the SNP, saying that they still wanted to break up the UK and couldn’t be trusted with the NHS.

“Mrs Sturgeon is announcing today that she is offering the hand of friendship to the rest of the people of Britain,” Brown said. “I know that that this means to offer the right hand of friendship to keep the left hand free to deliver the knockout blow to break Britain apart.



“Their only policy during the referendum was to cut corporation tax for the richest companies in Scotland by 3p, and the biggest beneficiaries would have been SSE and the other privatised utilities.”



Brown, who is standing down as an MP on Monday, said: “The surest way to get a Labour government is by voting Labour, and not voting for someone else.”

With polls consistently predicting an SNP landslide in May at the expense of Scottish Labour, Westminster parties and some parts of the media have ramped up the “sinister” nationalist threat. Over the past week, Sturgeon’s predecessor Alex Salmond has threatened both to lock the Tories out of power and to exploit Labour weakness in a minority government.



In the conference hall, the mood was upbeat but conciliatory, with the SNP’s Westminster leader Angus Robertson telling delegates: “We will play a constructive role in Westminster and bring our ideas forward in a positive spirit. We will offer a real alternative to the drab Tory-Labour cuts consensus.”

Asking for a show of hands from the conference floor to identify how many new members were present after the announcement that the SNP had reached an unprecedented 100,000 members earlier this month, the majority of arms shot upward.

The momentum provided by this army of dedicated new recruits was evident as Robertson announced that the party had already conducted its millionth doorstep canvass of the campaign, while the 10,000,000th leaflet since the start of the year was about to be delivered. MEP Alyn Smith revealed to cheers that the London branch of the SNP now has more members than the Scottish Liberal Democrats.

Opening the conference, the minister for Europe and international development, Humza Yousaf, told supporters that Labour has abandoned them. “Let us send out the message loud and clear,” he said. “There are no Labour heartlands any more.”