Pulp wrap up their reunion with an emotional swansong at Sheffield's cavernous Motorpoint Arena.

Backstage at the Motorpoint Arena in Sheffield, two huge, shaven-headed roadies are watching Jarvis Cocker cavort around the stage, throwing himself off speakers and whipping the crowd into a frenzy with every thrust of his impossibly sharp hips. Eventually, during the long, strange intro to 'Party Hard', one turns to the other, a baffled look slapped across his face. He tilts his head towards Jarvis and mutters: "There's something not quite right about him."

Some 34 years since Jarvis formed a band during an idle moment in a boring economics lesson, Pulp remain pop's elegant outsiders. They're still the band every mis-shape, mistake and misfit in the country see themselves in. When they stepped in to replace headliners The Stone Roses at Glastonbury 1995, Jarvis told the crowd: "If a lanky git like me can do it, and us lot, yeah, you can do it too." Their underdog triumph made it cool to be different.

But all things must pass. Rumours abound that this will be their final UK show, with all that remains on their tour calendar being a pair of dates on the Coachella Cruise, a floating hipster festival heading to the Bahamas and Jamaica, some way from chilly South Yorks. It's extra cold tonight, as they're playing at the home of the Sheffield Steelers ice-hockey team. The rink has been covered over with chipboard flooring but it's still there, frozen under their fans' feet. Pulp are being put on ice.

The weather hasn't deterred the hardcore fans, who've been showing up since 8am. Someone brought a marker pen to write the order they arrive in on their hands - that way they can huddle together for warmth but still keep their places in the queue. One fan is wrapped in silver foil, like a collapsed marathon runner.

The first to arrive is Melina, who has flown over from Georgia, USA just to see the show. "It's my first time in the UK," she says. "I first saw Pulp on television when I was 15. I fell in love there and then." She's one of many international fans who've made the pilgrimage, knowing this could be the last chance to see their idols.

The fans are younger than you'd expect for a reformed Britpop-era group. Another early arrival is Alice, who at 17 has been alive exactly half the time that Pulp have been a band. "When I saw them at Reading Festival it changed my life," she giggles. "I can't wait for 'This Is Hardcore', when Jarvis does his thrusting." Another fan, from Australia, sums up why Pulp are the sort of band worth queuing all day for: "It's because of the people that Pulp write about. You don't hear about people like me unless you listen to a Pulp song."

There are 12,000 people at the Sheffield Arena who feel the same way, so Pulp have to work hard to make the show feel intimate. Before the band go on, drummer Nick Banks says: "We're going to play all the ones they want to hear, so I don't think they'll be leaving disappointed, but hopefully they'll also hear some stuff they might not have heard for a long time - or even ever."

Against the odds, Pulp manage to transform this cavernous sports warehouse into a local club. They have a fake fireplace onstage, beside which Jarvis nonchalantly sips red wine. The best moment is what Jarvis describes as toilet-paper-powered "time travel". In the band's early days they would festoon venues with rolls of it, in lieu of the pricier pyrotechnics they can deploy today. After inviting the audience to cover the whole arena in long white paper streaks of the stuff, they reach way back into their collective history fishing out 1983's 'My Lighthouse', accompanied by Jarvis' sister Saskia; 1985's brilliant 'Little Girl (With Blue Eyes)'; and 1991's disco-dancing 'Countdown'.

Longtime collaborator Richard Hawley joins them for a chunk of the set, notably when he plays the solo on 'Born To Cry' live for the first - and possibly last - time. He won't be joining the band for their cruise-ship shows, so tonight is particularly poignant for him. He says later: "I'll be seeing them off with a tearful hanky at the pier, but it seems fitting to wave them off into the sunset."

Hawley knows Pulp won't be forgotten: "The only shame about them not doing anything new is that they could put a real spin on what's happening in our country and the fuckwits that lead us, although in a way it's already been said with songs like 'Common People'," he says. "Jarvis' lyrics aren't just of a period in time, they still make sense. We've still got cunts in charge. As long as there are dickheads like Cameron and his ilk, Pulp will have relevance. Their songs go beyond political ranting to something far more subtle and important."

Later in the night, at Pulp's party for friends and family at The Blue Shed, you can see the baton being passed to a new generation. Pulp bassist and Palma Violets producer Steve Mackey hugs his proteges as Arctic Monkeys tunes blast across the dancefloor. Chilli from the Palmas is full of praise for their mentor: "Steve Mackey is a king! I saw Pulp at Hyde Park, but tonight was the one! This was a whole different level." Emmy The Great says tonight's performance was among the best she's ever seen: "I saw a girl with Pulp written on every inch of her body weeping at the end. I understood because that's how this band makes people feel."

After the gig, Jarvis hosts a small party in his dressing room. It's a chance to ask him what it meant to return to play in Sheffield. "The thing is," he says, wine glass firmly back in hand, "even though I haven't lived here for a very long time I always get in a right fluster when we come to Sheffield. Tonight was no exception. Your mother's there, your sister's there - even onstage singing with you. I think we made a connection. The toilet rolls were good. We were trying to take this shed and make it feel like an intimate Sheffield thing."

So the only remaining question: is this really it, Jarvis? The last ever Pulp show on terra firma? "Ooh, I cant..." He cracks a smile and trails off. "Certainly for a while, yeah. I don't believe in saying that it's the last one forever. There was enough pressure on tonight without saying: 'This is it: the final show.' It's not really our call. When we played at [South Yorkshire arts space] Magna, it felt like, 'Ooh, right, this is the end.' You can try to tie everything up neatly, but you just have to see what life throws at yer. That's the way life works. You can't impose a structure on it. So... we'll see. But this is it - for now."

Pulp will soon be heading back to their day jobs. But what are they, exactly?

Jarvis Cocker He's released a pair of highly acclaimed solo albums, but these days he's more likely to be found in the BBC 6 Music studios recording his Sunday Service programme.

Candida Doyle Having occasionally played keyboards for Jarvis in his solo incarnation, Doyle also travelled the world and trained to become a counsellor last time Pulp went on hiatus.

Steve Mackey Having previously produced everyone from MIA to Florence + The Machine to Palm, Mackey will be going back into the studio with Palma Violets as they put the finishing touches to their debut album due in February.

Nick Banks The only member to still live in Sheffield, he'll help run the family business - Banks Pottery, specialists in crockery for hotels.

Mark Webber An avant-garde filmmaker, Webber is curating a BFI tribute season to Lithuanian director Jonas Mekas.

Director Florian Habicht is making a Pulp concert movie

How involved has Jarvis been?
Florian: "He had a concept for the film and it really gelled with my ideas. I wanted to make a film where real people are the stars. It's not a rockumentary where there are celebrities going on about how great the band are. It's about capturing real people, which is kind of what Pulp's about."

When did you first get into Pulp?
"I was making a film and I had a friend, Jackie, who was a dancer and she did this really weird sexually fucked-up solo dance to one of their songs, 'Bar Italia'. I just fell in love with them at that moment.

Is this your first time in Sheffield?
"Yeah. There are lots of special people here. I met a really great psychic who said I should be out there filming people. He said, 'Don't film the band, film the people'."

So we shouldn't expect an ordinary concert film?
"I've just been outside filming the people queuing up and they might get more screen time than the gig itself. We're just getting a whole lot of magic and then we're going to shape it and knead it. It'll be a concert film like you've never seen before.