Preparing to shoot a crowd scene for the video to accompany the England squad's Euro 96 song "Three Lions", they are all too well aware of the impossibly naff history of football pop singles. Images of Kevin Keegan, bobble-perm flapping uneasily as he bobs along to "Head Over Heels in Love", are hard to erase.
But despite the irreverent tone of Fantasy Football, the BBC2 programme they host, Skinner and Baddiel are taking the project seriously. In between shots, Pedro Romhanyi, the director of Three Lions, assures me of their good faith. "They treat football with respect," he says. "This is not about making a pop video; it's about doing something that's good for football."
While waiting for Geoff Hurst to turn up for the next sequence, Skinner, Baddiel and Broudie wander down to the nearby dockside. All kitted out in personalised England shirts ("in South London you have to put your names on all your clothes or they go missing," Skinner quips), the trio perch by a monster crane and expand on why they're doing the song.
Broudie, whose work has often been used on Grandstand, was approached by the Football Association, and he in turn approached Skinner and Baddiel. They hit it off immediately.
The whole project - music, lyrics, video - had to be vetted by the FA. In addition to the single and the video, bands such as Blur, The Beautiful South, Black Grape, Massive Attack and Supergrass are contributing to "The Beautiful Game", the authorised tournament album.
"The fact the FA let us do it at all shows a lot of balls on their part," Baddiel said, "but they felt that Fantasy Football was essentially a good thing."
"Although we couldn't have done a song called 'Let's All Go to Luxembourg and Set Fire to a Wine Bar'," Skinner added, quick as a flash.
"We didn't want the song to be saying: 'We'll definitely win and everyone is frightened of us'. Everyone is, but that's because of the supporters rather than the players," Skinner continued. "We wanted to acknowledge that we had had some hard times, but now it's a time for optimism. It's not poncey to be optimistic."
Skinner passes the conversational ball to his flat-mate - on and off screen. "The song is aware of the negative aspects of being an England football fan," Baddiel said. ''The key line is: 'Thirty years of hurt never stopped me dreaming.' We're setting ourselves up against people who knock England. It's OK to hope we'll do OK."
The song roars with patriotism and the writers have included specific allusions to gee up even the most jaded armchair cynic.
I still see that tackle by Moore
And when Lineker scored,
Bobby belting the ball
And Nobby dancing.
"The aim was to isolate some moments which will raise goose pimples on the back of England fans' necks." Baddiel said. Skinner, Baddiel and Broudie experienced some goose pimples when they went to a recent Bisham Abbey training weekend to explain the song to the England squad. "It was nerve- wracking," Skinner said. "We were having lunch with the players and, when we got to the cheesecake, Gazza couldn't wait any longer and went to put the song on. Fortunately, he was unable to operate the cassette-player."
Baddiel dribbles along with the story. "At first the players showed no more enthusiasm than occasionally tapping a fork against a plate. Then we explained the song as if to a group of three-year-old children and they got it. Terry [Venables] was particularly positive about it. 'Roll on, 8 June,' he said. It's all about the tradition of playing for England, and Terry's someone who'll respond to that."
They went to fulfil every schoolboy's - and most adults' - dream by having a kickaround with the England team. Still starry-eyed, they rounded off their day by recording the chorus with the squad. "Unfortunately Alan Shearer was injured," Baddiel laments. "He was holding something back because you have to sing from the groin."
Skinner chipped in. "If Matt Le Tissier had been there, he wouldn't have sung anything for three verses, and then suddenly he would have come out with something brilliant."
Skinner and Baddiel may take the rise out of footballers - after they sent up Nottingham Forest's Jason Lee, they were condemned as "middle- class wide boys" by his manager, Frank Clark. On this project, however, the duo are supporters first and comedians second. "At heart, we're genuine fans," Baddiel said.
"We're like kids in a toy shop with professional footballers," said Skinner, who is so devoted to West Bromwich Albion that he had videos of all their games sent out to him when he was touring North America.
A week after the Bisham Abbey kickabout, Broudie, a lifelong Liverpool fan, is still in Scouse heaven. "In the line-up for the song, I was between Robbie Fowler and Steve McManaman," he said, beaming at the memory. "I was like the cat that got the cream. I couldn't stop smiling. At the end of the day, my mouth was hurting."
The single, "Three Lions", and the album, "The Beautiful Game", are released on Monday. The video "Fantasy Football III: Two Men and a Football" is released on 3 June.