It's a Friday afternoon in the transport hub known as Hull Paragon Interchange, and Peter Mandelson is admiring a statue of that local icon Philip Larkin, while paying tribute to the poet's singular view of life. "He's quite interesting about sex," he says. "He said the thing about sex was it was too good to share. He also said, oddly, that sex is a bit repulsive – like asking somebody else to blow your own nose. And he's sort of right in a way, isn't he?"

At that instant, a woman clocks the famous visitor, and pays him a backhanded compliment. "You've really changed your image," she says, with an air of surprise. "You're a very attractive man." He cracks a smile. "Perhaps we're not going to just see the transformation of Hull, but the reinvention of the Prince Of Darkness."

Perhaps we are. In February this year, Hull city council appointed Lord Mandelson to the role of high steward. The post was created in 1583, and fell into disuse during the 1970s, but has now been revived, along with the role of high sheriff, a post awarded to the former Tory minister Virginia (now Baroness) Bottomley. In the case of this former business secretary and EU trade commissioner, his title has a whiff of the hereditary principle: between 1956 and 1965, its holder was his grandfather, the esteemed former Labour high-up Herbert Morrison.

"My role is to be an adornment," he says. "An ornament. But also to be an ambassador and an advocate for the city: to use my sharp elbows and my networks to do what I can to project it, promote its interests and bring investment and jobs. The city has got to rediscover itself and reinvent itself. It needs a series of major transformational moves."

Two initiatives symbolise what he is talking about: the recently introduced "Hull city plan", aimed at bringing in £1bn of investment and creating 7,500 jobs – and Hull's bid to become Britain's official city of culture in 2017, an honour for which it is competing against Leicester, Swansea bay and Dundee.

Since the decline of its fishing trade in the 1970s, Hull has had rather a faded atmosphere, something increased by deindustralistion and, lately, the effects of the financial crash, symbolised by an apparently huge number of empty shops. Two years ago, it had the UK's highest proportion of working-age residents who were unemployed, and issues of joblessness and the scarcity of opportunity are still palpable. But talking to people in the city centre, there's also a sense of unlikely optimism, and the belief that we are now somehow over the worst. Whether this is based on anything concrete is a moot point – "In the paper, they say it's getting better, and you have to think positive," one woman tells me – but the feeling seems real enough.

In Britain's boom years, there was regeneration and redevelopment here. For Mandelson, the big prize is the possibility of a wind turbine plant run by the German company Siemens, which he says is looking 80% certain. Today, though, is all about Hull's city of culture bid, so he flits around a handful of landmarks, engages with the public in the manner of a seasoned pro and explains what he's doing in terms so simple as to sound almost banal. "If you've been in politics as long as I have, you want to carry on doing something important and relevant. And they gave me the chance, so here I am. It's no more complicated than that."

We begin at the city's docks and make our way to the former fruit market, now the location for a burgeoning local bohemia centred on a gallery, pop-up businesses, a recording studio and rehearsal rooms, where Mandelson watches an accomplished local band called the Hubbards. There is talk of the cultural titans associated with the city: Larkin, the actor Tom Courtenay, David Bowie's guitar player Mick Ronson, 1980s indie kings The Housemartins, and Everything But The Girl, who came here as students. He also pays tribute to the place's entrepreneurial derring-do – "What I like about it is the confidence: the buoyancy of the place" – and climbs into the cockpit of a rickshaw, which he almost crashes into a parked car before pedalling away to the nearby marina.

Most of the time, he is in full city-ambassador mode. "Hull would receive a huge lift if it became the city of culture," he says. "It would be a recognition of everything that's being done: all the changes that have been made, and the creativity. That'll still happen if we don't become the city of culture, but my God – wouldn't it make it all worthwhile?"

We end the afternoon at the new premises of the Hull Truck Theatre company, a cultural institution of 42 years standing, synonymous with the work of local playwright John Godber. Mandelson watches a rehearsal for a new play called Jumpers for Goalposts, one of whose songs is taken from those kings of northern melancholia The Smiths. Sung by a lone member of the cast, it is a moving hymn to what Hull, with the former Prince of Darkness's help, is trying so hard to achieve: "Please, please, please, let me get what I want/Let me get what I want, this time."