“The door is closed to Labour in Blantyre,” came the mocking cry from the Yes campaigner standing on the pavement outside the house where Ed Miliband was awkwardly waiting for a response to his knock.

The former mining town, eight miles south-east of Glasgow, where Labour founder Keir Hardie was born, was the perfect symbolic location for the the party’s current leader to appeal to core voters to reject the idea of Scottish independence. But things are not always so straightforward.

In a speech at Blantyre Miners Community Resource Centre on the subject of social justice, Mr Miliband told supporters that Scotland would only be made fairer if the country voted No and then elected a Labour government. “We can build a more just Scotland within a more just United Kingdom. True to the traditions of our pioneers, true to the traditions of the heroes of Scotland,” he said.

Stating that it was a “very important moment” in the campaign, Mr Miliband announced that Labour was sending some of the party’s big hitters north next week to rally support and attack First Minister Alex Salmond’s policies on social justice, such as the cutting of corporation tax post-independence.

The offensive will feature Ed Balls and Baron Prescott, and will culminate in a major rally in Glasgow next Friday, where Mr Miliband will be joined by the former prime minister Gordon Brown and Scottish Labour leader Johann Lamont.

It is a drive that the party badly needs – but some argue it is already too late. There is strong evidence that growing numbers of traditional Labour supporters are intending to vote Yes in the referendum, angry at how the party has aligned itself with the Conservatives on certain issues. A YouGov poll this week revealed that support for independence among Labour voters had risen from 18 per cent to 30 per cent in the past month. A Blantyre passer-by distilled the party's problem into a two-word insult: “Labour Tories!”

One lifetime Labour supporter at the speech, who declined to be named, said Mr Miliband should stand down as leader in the event of a Yes vote. “I think he’s a nice chap, but a lot of the MPs they’ve brought in up here are not streetwise. You have to be able to talk to people on the street and be able to understand what they’re saying,” she said.

Asked by The Independent if he would consider resigning as leader if Scotland voted for independence, Mr Miliband replied: “It doesn’t matter. We’re fighting to win this referendum and I believe that’s what’s going to happen. This is not about any one individual, this is a big question for Scotland.”

Other voters in Blantyre were less than charitable about the party’s decline in its former heartland. “We’re all ex-Labour supporters – but now they’re just Tories in red ties,” said Tom McQuade, who was holding a Yes placard.

“Mr Miliband’s come up today to a place he doesn’t even know – he probably couldn’t even put a finger on a map of where it is. He told us two months ago he’d come up to Scotland and spend the last six weeks living here. But they never even told us he was coming to Blantyre today.”

He added that “90 per cent” of people in Blantyre were still Labour supporters, but claimed that the “vast majority” would be voting Yes on 18 September. “Very few will come out and say it, because it’s not what Labour want them to do, but when it comes down to private and personal voting, they’ll be Yes,” he said.

Organisers of the event complained that a group of dedicated independence supporters had arisen in the early hours to remove all the No Thanks signs from lampposts around Blantyre when they heard Mr Miliband was on his way. In the battle for Scotland’s hearts and minds, it looks like the Labour leader has his work cut out.