ACCORDING to the tour guides at Glasgow City Chambers, the most unusual visitors since Queen Victoria opened the building in 1888 have been the Cybermen.

A pair of the metal killing machines were filmed for a recent Doctor Who episode clanking down the Carrara marble staircase that transforms the centre of the place into a light-filled grotto inspired by the Italian Renaissance.

These days the mahogany-lined rooms and tiled halls running off the main atrium echo with reports of an even more unlikely alien invasion: the SNP aim to touch down in George Square.

Once regarded as the Kremlin on the Clyde, Labour’s impregnable bastion in the west of Scotland is facing its first credible threat from the Nationalists, thanks to the SNP’s spectacular success in the Holyrood election.

Beyond the kudos of running the biggest council in Scotland, the SNP – if successful – would displace Labour in their heartland, and reach a vital staging post towards independence.

For if Alex Salmond is to win his referendum, he has to take Glasgow with him. The city is the pivot on which his dream turns.

It all means that after decades of stifling political monoculture, life in the chambers is getting very interesting again.

But this is more than just a straightforward battle between the red corner and the yellow.

Beneath its alabaster skin, the chambers are home to the kind of warped passions – paranoia, revenge, ambition – which would be as familiar to the Medicis and the Borgias as its architecture.

So poisonous is the atmosphere, no-one from either party wants to talk in the open.

The busy tearoom where the gossips jump to conclusions over their subsidised lunches is categorically off limits.

Instead, all the interviews have to be held behind closed doors or off the premises.

In this political psychodrama, both protagonists are dysfunctional and divided, but each has a redeeming shot at glory.

The SNP are on the up, Labour on the slide.

But the SNP lack a leader, while Labour have one many in the party would like to cast aside.

Since the 2007 election, the SNP have suffered two defections and been split by the behaviour of their leader, James Dornan.

He was promoted by SNP deputy leader Nicola Sturgeon, but was seen by some in his group as more interested in a billet at Holyrood than the daily grind of the chambers.

Dornan got his wish on election night when he became MSP for Glasgow Cathcart.

But his move east leaves a vacancy at the top of the group which is due to be filled on June 6, with the possibility of yet more infighting.

Labour are even more fractious.

In the wake of Steven Purcell’s resignation as leader last year amid revelations of cocaine use and a drink problem, the party’s councillors chose Gordon Matheson as their new boss.

But instead of unity breaking out, a faction promptly coalesced round the loser, Paul Rooney. It has hoped to dislodge Matheson ever since.

Since the New Year, this group has strained Matheson’s workload to breaking point, picking needless fights in an attempt to undermine his authority and perhaps sicken him into quitting.

Just before the Holyrood election, it looked as if Matheson might be challenged for the leadership at the Labour AGM later this month.

The scale of Labour’s losses on May 5 seems to have shocked councillors into calling a truce on their civil war for now.

“There’s nothing like a hanging to concentrate minds,” observes one Labour source.

However, Matheson’s rivals could be biding their time, waiting to blame him for a bad result in the Scottish council elections in 2012 before going in for the kill.

Throw in rumours of behind-the-scenes meddling by Purcell and moves by Labour powerbrokers such as former MP Mohammad Sarwar and businessman Willie Haughey, and it all means Matheson is under huge pressure to deliver a win for Labour.

It’s only the Union at stake, after all.

Against such a giddy background, it can be hard to focus on the basics, but Graeme Hendry and Billy McAllister, the head and heart of the SNP group respectively, are trying their best.

Currently deputy leader, McAllister was one of the first to beat Labour where they lived, winning a breakthrough by-election in Maryhill in 2006.

“They said I didn’t have a hope in hell, they laughed at me,” he recalls with a grin in the SNP’s spartan third-floor office. “Now look.”

He predicts Labour are “in for a doing” after taking voters, especially the poor, for granted.

“The only people Labour have lifted out of poverty is themselves – MPs and MSPs sitting on £50,000, £60,000, and living the life of Reilly while their constituents are rolling about for scraps. People are sick and tired of it.

“Labour are a spent force. They have no ideas.

“They’ve sat on their laurels for years shouting about the Welfare State, that it was started on their watch, but you can’t keep living on that.”

Like his SNP colleagues, McAllister, 58, is acutely aware of the city’s wider significance.

“It’s all right winning rural seats but if you want to go for full independence, this is where it will be won or lost. I can see it just around the corner, I can see it in my lifetime now.

“That’s the difference between us. We’re hungry and we want our country back. We want to be in charge of our own destiny. Labour don’t have that hunger any more. That’s their downfall.”

Labour were last out of power here in the late 1970s, when the SNP supported a minority Tory administration on the old district council. After that Labour were utterly dominant

It wasn’t until the arrival of the proportional STV voting system in 2007 that the SNP, Greens and Liberal Democrats arrived in any numbers.

Even then Labour still won an overall majority, making it one of just two councils in Scotland, alongside North Lanarkshire, where Labour retained absolute control. But the SNP’s Holyrood triumphs have changed the electoral calculus again.

Not only did the SNP win five of the city’s eight seats, including totems such as Shettleston and Anniesland, they out-polled Labour on both the regional list and in total constituency votes.

If the local election had been the same night, the chambers could already be in SNP hands.

Although a good result at one poll doesn’t ensure a similar result at the next, the SNP sense there is now a national tide running which can sweep Labour from Glasgow.

But first the local party have to find a new leader, not just one who can head an opposition, but one capable of running the administration and a £2.3 billion budget next year.

Three candidates are standing to replace Dornan, all elected for the first time in 2007 – Allison Hunter, Nicola Sturgeon’s election agent; Phil Greene, a former social work officer; and Kenny McLean, a former aide to MSP Sandra White.

McLean is an early favourite, but Hunter could act as caretaker until, as expected, she steps down next spring.

She could also be the “unity candidate”, bringing together the pro- and anti-Dornan factions.

Labour sources say Greene is the most talented, but that could be a double bluff on their part.

With so much potentially riding on the outcome, it is almost inconceivable Sturgeon will keep out of the selection, so it could get messy.

An interim leader would also be bound to prompt Labour claims that the SNP are asking voters to buy a pig in a poke next year.

The SNP need a new election strategy too.

Afraid of over-reaching themselves under STV, the party only fielded 22 candidates in 2007.

All were elected, but an absolute majority in Glasgow means having 40 of the 79 councillors, so the party need to change tack.

Earlier this year they decided to run exactly 40, but since May 5 that has become a minimum.

However, with four or five of their councillors stepping down next year, if the SNP does win, more than half and possibly two-thirds of their councillors would be wide-eyed novices.

To make sure they’re kept busy and don’t go astray, the SNP are now having to think like an administration in waiting, drawing up plans which they can put into immediate effect.

Hendry, who led the charge against sleaze at Strathclyde Partnership for Transport, is working on a review of the council’s arms-length bodies and other “Labour fiefdoms”, and is also looking to shake-up the senior managers, some of whom he says have been “running riot” and defying the wishes of elected politicians.

“There’s a lack of respect between senior officers and the people running this ship that needs to change.

“That doesn’t mean a clear-out, but we do need to review if everyone fits in.”

In contrast to the SNP’s heads-down, sleeves rolled up attitude, he says Labour are dazed, divided and generally clueless after the election.

“I think there’s an instinct in them to go dirty [in the campaign]. They’re good at spending money but at the moment ... they’re really struggling for ideas.

“They also have a leader who’s pretty much a lame duck, someone who does not command respect within his own group, far less across the chamber.”

In his magnificent corner office on the floor below, Matheson frenetically denies his party is divided – that’s just “tittle tattle” he says – and insists Labour can win again in 2012.

Bobbing around in a leather armchair as big as a postcode, he declares: “There is nobody hungrier for winning next year than me and my team.

“I’ve only been in this job for one year. I’m not giving it up after two. The SNP see the winning of Glasgow as a stepping stone towards a referendum on independence.

“Well I’m sorry, we’re not prepared to be stood upon by the Edinburgh political establishment.”

However, he admits Labour could lose the city.

“Yes, we can lose, but we’re not going to ... We do not take success for granted, but I tell you what, I’ve got a proud record, a strong vision and a talented team.

“The SNP are squabbling over who’s going to be the next leader of their group.

“They don’t have the talent, they don’t have the experience, and they’re disunited. I’m not leading this group to defeat, I’m leading this group to victory.”

If voters disagree, a win for the SNP could yet be bittersweet.

Glasgow could become a billboard for SNP failures in Government and rash election promises.

If there are painful service cuts or compulsory redundancies, there will be no blaming Labour for it, and the concentration of media in the city means the problems would be projected nationwide.

But with the road to independence running through George Square, the SNP must take the risk.