The SNP is offering one hand of friendship to the UK with a fist behind its back to deliver the "knockout blow to break Britain apart", former prime minister Gordon Brown has warned.

SNP leader Nicola Sturgeon will today extend a message of "friendship and solidarity" to the rest of the UK in her keynote speech to the SNP conference.

But Mr Brown warned the SNP's only goal remains Scottish independence, during a campaign speech at Liberton High School in Edinburgh supporting local candidate Ian Murray.

He attacked the SNP for never proposing an income tax rise to fund the NHS and pledging to cut corporation tax.

However, Labour activists told how they are struggling to counter the message that the SNP is an anti-Trident party that will stand up for Scotland at Westminster.

One Labour activist asked how to respond to the SNP's "progressive" mantra, while another said "the SNP seems to be winning the rhetoric".

Mr Brown, who stands down as an MP on Monday, said: "Mrs Sturgeon is announcing today that she is offering the hand of friendship to the rest of the people of Britain.

"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."

Mr Brown said: "Who would you trust with the NHS ... the Labour Party that was prepared to go to the people of the country, as I had to do at the beginning of the century, and say: 'We have to raise taxes/national insurance so that we can pay for a better health service in the future?'

"Or the SNP or any other party in Scotland, who have never bothered to ask the Scottish people to put more money into the NHS?"

He continued: "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."

An aide to Edinburgh East MP Sheila Gilmore said: "Quite often people say to me: 'I've left the Labour Party, I'm not going to vote Labour, I'm voting SNP because we will get a bigger voice for Scotland at Westminster through the SNP. Even if there isn't a coalition it will vote-by-vote, this is the way to get inequality dealt with in Scotland.'

"What is the best answer?"

Mr Brown said: "The surest way to get a Labour government is by voting Labour, and not voting for someone else."

Another activist said: "The question I find difficult to deal with is Trident, because I am one of the Labour Party supporters who want to get rid of it.

"I would love to spend £100 billion on welfare. That for me is an area that I find very difficult when I am trying to convince people to vote Labour."

Mr Murray said Labour will put Trident into the strategic defence review for the first time "so it will be up to the defence themselves to decide what to spend the money on".

"Let's get away from talking about this £100 billion, it's a smokescreen for whether there is a morality issue over Trident," he said.

"I've always been for not renewing Trident but not on its own, it's got to be done as part of a commitment to global disarmament."