It is hard to find anyone in the Labour-held constituency who is intending to vote for the party at the general election in May

Waiting for fares by the newly opened Malmaison hotel, on Dundee’s sparkling £1bn waterfront redevelopment, taxi driver Ian Higgins has no doubt about the outcome of May’s general election: “I think it will be an SNP landslide and it will maybe wake up the politicians down in London who all seem to be out for themselves.”

The 62-year-old voted for the very first time in last autumn’s referendum and voted for independence, along with 57.3% of his fellow Dundonians, earning it the soubriquet “Yes City”. Higgins intends to vote again in May, unsurprisingly, for the SNP. “They seem to be doing more in the short time they’ve been in charge of the local council [since 2012] than Labour ever did,” he explains.

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What is surprising is how difficult it is to find anyone in Dundee West, one of the nationalists’ key target seats currently held by Labour’s Jim McGovern with a majority of just over 7,000, who is intending to vote Labour again.

New constituency polling by Lord Ashcroft suggests that Dundee West has experienced a 27% swing to the SNP in voting intentions since 2010. Wednesday’s poll, also finds a 21% swing to SNP from Labour across 16 constituencies suggesting a Labour wipeout in Scotland, and potentially ruling out Labour’s majority in Westminster.

It is evident to observers that for Scottish Labour’s new leader, Jim Murphy, time is motion. Since his election in December, his campaigning has been relentlessly dynamic, with new policy announcements – often framed to appeal to yes-leaning Labour supporters – emerging at an exhausting rate. Opponents may dismiss it as cynical; party insiders consider it an urgent and necessary strategy to remove every obstacle in the way of returning to the Labour fold in May.

But in Dundee’s Overgate shopping centre, where Murphy was heckled by yes supporters during his pro-union speaking tour last summer, the impact of Scottish Labour’s recent pronouncements on welfare, fracking or the Transatlantic Trade and Investment Partnership appears minimal. No one had heard about Labour’s calls for a Scottish government inquiry into the recently revealed overspend on the new Victoria and Albert design museum, one of waterfront’s flagship projects.

Adele Herron, who has just come from an interview for primary teacher training and identifies her main voting concerns as education and the NHS, says: “The SNP seem to be much more the party of social justice, especially since Nicola Sturgeon became first minister.” Just 18, and casting her first vote in a general election, Herron – who voted yes in the referendum – wants to read both manifestos carefully before making her decision.

Lunchtime shoppers can certainly identify Murphy’s photograph far more readily than that of their local MP.

Michael Scallion, taking a break with his partner and toddler son, agrees that he has noticed the new leader’s “greater presence”, although he wasn’t aware of the shadow cabinet’s visit to the city a few weeks ago.

“I think that Labour have hurt themselves too much,” says the 37-year-old, who intends to vote for neither that party nor the nationalists in May. “The majority of people have the perception that a Westminster elite is running everything so they don’t believe that Scottish Labour can be a separate party.”

In Labour-held seats, the proportion of voters who say they would prefer Ed Miliband to David Cameron ranges from 34 points to 42 points.

For all the talk of a Labour ground war, the percentage of voters who say they have been contacted by Labour in the past few weeks is in single figures in Labour-held seats.

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The exception is Anas Sawar’s Glasgow Central seat and the Renfrewshire seat of Douglas Alexander. It is possible that the low figure reflects the Christmas holidays, since the polling was conducted from early January.

But the SNP clearly has a higher contact rate than Labour, underlining the extent to which the once mighty Scottish Labour electoral machine has declined.

The poll found broadly a quarter of current SNP supporters did not rule out voting Labour, but a third of Labour supporters did not rule out voting SNP, suggesting more of the Labour support is vulnerable than that of the SNP.

What is striking in Dundee West is that people’s disaffection with Labour is local as much as national. Many reference council corruption under Labour. There has been a change in culture, too. As one man tells me: “Gone are the days when people said they were voting Labour because their parents voted Labour.”

For all the diversity of contributions to fields ranging from medical research to video games that led Dundee to be recognised as the UK’s first Unesco City of Design in 2014, locals raise concerns about the widening health and educational gap between the poorer and more affluent areas of the city. More than a quarter of children in Dundee are growing up in poverty.

Lochee, to the west of the city centre, was once home to the largest jute mill in the world and now deals with the inevitable consequences of de-industrialisation. At Sew Creative, one of the few independent businesses to survive on a high street that has been overtaken by bookies and charity shops, Margaret Duncan explains that she has been a nationalist all her life but only recently re-joined SNP.

“Lochee used to be staunchly Labour,” she says, “but not any more. I don’t even know what my MP looks like. They’ve left themselves wide open, especially now that people have seen what the SNP are doing on the council.”

The previous day, Duncan met the newly selected SNP candidate for Dundee South, Chris Law. A pony-tailed local businessman, Hall rose to prominence during the referendum campaign when he used a reconditioned Green Goddess fire engine to distribute pro-independence literature. “He’s different,” she says, “and he’s what we need. He listens to people and he’s more from the grassroots.”

But the referendum by no means informs everyone’s voting intention. Kenny Cassidy, a former Inland Revenue worker who voted for independence, says he will be voting Labour “through gritted teeth”.

“Nationally, they’re all different shades of the same thing,” says Cassidy, “but the SNP is not a political force in Westminster.”

Meanwhile, Cliff Robertson, owner of the nearby sweet shop and a no voter in the referendum, says he always voted Labour in the past, but is now sitting on the fence. “This has always been a Labour neighbourhood but more and more people are thinking about the SNP,” he says.