Duct tape, cork tiles, plastic valves from the local hardware shop and a DIY spacesuit are just some of the items strewn around the old submarine berth in Copenhagen's dockyards. Think "space programme" and you probably imagine high-security rocket launches and multibillion-dollar technology. What you may not picture is a bunch of enthusiastic amateurs tinkering with an eight-tonne rocket that may one day launch a man into space.

Peter Madsen was 10 years old when he watched the Space Shuttle Columbia's first flight on TV in 1981. "I remember being fascinated by the white plumes of steam and the shockwaves of the hydrogen fuel," recalls Madsen. "From then on, I was hooked."

This was a problem for a boy living in Roskilde, Denmark. "There isn't exactly a Cape Canaveral out here, so I got into amateur submarines instead – they're a lot like rockets in many ways," says Madsen, who learned to assemble submarines from scratch and became famous for building a 40-tonne sub with friends for just £125,000 in 2008. "I did a newspaper interview at the time and the journalist asked what I was doing next, so I said I wanted to build a rocket. As soon as the article came out, this guy emailed, saying he could help."

The Copenhagen Suborbitals team at work. Photograph: Jev Olsen

Aerospace scientist and fellow Copenhagener Kristian von Bengtson was working on Nasa's Constellation programme but had become disillusioned by the notion of space as big business. "Every decision had to go through boards, sub-groups and committees – it was more bureaucratic and political than I'd expected and when a new president came into power, projects got scrapped," says Bengtson. "I knew of Peter's work already so when I read he wanted to go into space, I got in touch."

The pair met for coffee and within 10 minutes had sketched out a plan for a rocket they thought they could build – on a shoestring. "We wanted to put a human in space in a new way and without lots of money – to be in the workshop every day, instead of in meetings with banks," explains Madsen. The not-for-profit Copenhagen Suborbitals was born.

"We started work straight away in a submarine hangar and ran a test flight two years later," says Madsen. Since then, they have notched up successes with the most powerful amateur rocket ever flown and the first amateur rocket launch with a full-size crash test dummy in it. Now, they are working towards their first manned space flight above the Kármán line, the border between Earth and outer space. If they manage it, they will be the first amateurs to make it into space without government funding.

In the last month, Bengtson and Madsen have passed another major milestone – creating their DIY spacesuit for a volunteer astronaut to wear on the rocket's first flight. Whereas a Nasa-style spacesuit can set you back in the region of $12m (about £7.5m) Copenhagen Suborbitals needed to create something safe and durable on a fraction of the budget. "We have around 1,000 supporters, each paying 100 kroner a month [about £11], as well as 46 part-time volunteers," says Madsen. We do events and talks to raise extra money, but really it's about keeping costs to a minimum."

This is achieved by following the Copenhagen Suborbitals philosophy of using simple solutions for complex problems. "The DIY spacesuit is made with valves and pipes from the hardware shop," says Bengtson, "because there was nothing to suggest these wouldn't work just as well for our purpose as some fancy equipment. We use a lot of stuff you can buy in the supermarket or local shops." He is using cork from the nearby carpet shop as a heat shield in the rocket.

One of the Copenhagen Suborbitals team. Photograph: Jev Olsen

Without access to specialised space facilities, the team trooped down to Copenhagen hospital and persuaded bosses to let them have a go in a hyperbaric chamber, normally used to treat divers suffering from decompression sickness. With a medical team on hand and a hopeful crew of space enthusiasts looking on, a volunteer allowed himself to be strapped into the home-made suit and stepped in to the pressure chamber. "We created 0.6 bars of pressure – the equivalent of going up to 13,000ft," Bengtson told the Guardian after the test day, "and luckily, the suit worked."

The Suborbitals were similarly thrifty when it came to testing out the astronaut's capacity for g-forces. "We didn't have the money to hire Nasa's facilities so we went to Copenhagen's Tivoli Gardens and tested the g-forces on fairground rides instead," says Bengtson: "Turns out the Vertigo ride has exactly the same g-force as our rockets, so we hired it for a day."

Family and friends are supportive and Madsen's wife recently got a tattoo of him in the spaceship – "so she's totally behind this", he says. Bengtson's family have also embraced the project, though as a father of two young sons, it has been agreed that he will sit out the first manned rocket flight. Madsen will wear the DIY spacesuit on the maiden voyage. "It's such a buzz every day, even before I get into space. The flight will be something else," he says.