Election Constituency Profile: Edinburgh East
But Edinburgh East is now seen as the most vulnerable constituency in the city to the SNP’s apparent surge.
It is a clear contest between the two parties. The Nationalists won the equivalent Holyrood seat in 2007, four years before the party’s landslide.
And in last year’s independence referendum Edinburgh East recorded the biggest Yes vote in the city at 47 per cent.
Ms Gilmore admits the result will be “a lot closer than last time”, but says: “We’re in this to win and hold the seat.”
And she adds: “There are quite a lot of people still taking a bit more time to make up their mind.”
Edinburgh East includes Portobello, Craigmillar, Prestonfield, Duddingston, Restalrig and Craigentinny, but also stretches right into the city centre and the Old Town.
Ms Gilmore, who took over as MP from Gavin Strang in 2010, says the election should not be seen as the referendum mark two.
“We’ve had that and 55 per cent of Scots said No. We should be getting on and talking about what we want to see at UK level, on jobs and job security, and also the Scottish dimension of how we are going to use the powers that are on their way or there already.
“When you talk to people, often they don’t even know there are new powers for the Scottish Parliament – it’s not something the Scottish Government wants to talk about.
“Additional borrowing powers are already in place – I’ve suggested these could be used to double our spending on affordable homes.
“And they have powers from next year over half the income tax rate, but there is no debate from the Scottish Government about what it wants to do with those powers.
“The whole debate about Scotland and more powers is very abstract, when there are things we could be doing now.”
Ms Gilmore also argues Scotland is sometimes too complacent. “We’re in a political climate where people are quick to say everything in Scotland is fine.”
In fact, she says, there are problems that need to be addressed. She cites an elderly constituent who had to wait almost all day for an ambulance to take him to hospital and widespread concerns about social care and how much time carers can spend with clients.
“These are serious issues and we need to start talking about how we resource them.”
SNP candidate Tommy Sheppard, founder of The Stand comedy venue, is optimistic about his chances, but says he is taking nothing for granted.
“If the election was today, I think I’d win,” he says. “But three weeks is a long time in politics.”
Mr Sheppard says his canvas returns are in line with the national polls, which show the SNP on course for a sweeping victory.
“There is a referendum legacy,” he says. “A lot of people who feel very disappointed in Labour and the role it played in the referendum.”
Many traditional Labour supporters voted Yes in September and he claims there is little indication of them returning to the fold.
He argues the party has lost voters by being too dismissive of those who were voting Yes.
“I’m old enough to remember the  Common Market referendum when Labour and the Tories both had Yes and No campaigns – so even though Labour had a policy in favour, it still tolerated dissent. The fact that was not allowed in the independence referendum probably has not done the party any favours.”
He says there is also a general alienation with Westminster politics and people who are not natural SNP supporters see the party as the one most likely to stand up for Scotland within the UK.
“Then you overlay that with specific issues – in some areas of the constituency, austerity is biting really hard and people are feeling the poverty; fracking is a big issue in Portobello; and the SNP’s Trident message is very much in tune with the electorate.
“People talk about education or health or policing or crime, but there seems to be a general sense that’s not what this election is about – this election is about the bigger questions of changing the overall economic direction, standing up for Scotland and making sure Scotland’s voice is not suppressed.”
But Mr Sheppard emphasises he is not confining his campaign to Yes voters.
“All my literature starts ‘Whether you voted Yes or No...’
“A lot of people who voted No are disappointed with what happened next and feel a little cheated. They still might not want to vote Yes, but they will vote SNP to get some assurance over more powers.”
The Scottish Greens have declared Edinburgh East their “national target” at this election. The party secured five per cent of the vote in 2010.
Mr Sheppard says he likes the Greens, but claims they are really more interested in next year’s Holyrood election than seriously contesting this one for Westminster.
“There is a big awareness among Green supporters they should lend their vote to the SNP if they want to oust the incumbent,” he says.
But Green candidate Peter McColl, former rector of Edinburgh University, sees it differently. He says: “There are a lot of people who just won’t vote for the SNP and won’t vote for the Labour Party. We’re there to give them a chance to vote for a progressive party which is against austerity, in favour of public services in public hands and wants to return power to people in communities. That’s our aim.”
Lib Dem Karen Utting says her party still has “good pockets of support” in the constituency which are “holding up well”.
Ayeesha Saleem, of the Trade Union and Socialist Coalition, says people are angry with politicians and she is standing so people can vote for “a different sort of society”.
And Ukip’s Oliver Corbishley says he is taking the opportunity to promote his party’s policies, including the “citizens’ initiative” where two million signatures would automatically trigger a referendum on any issue.