H&M is not just a big player in "fast fashion", it's a giant. Estimates (fast fashion behemoths do not give out many production figures as the sector is intensely competitive) suggest it sells more than 550 million garments every year. It recently announced net quarterly profits of $412m. It is second only to Inditex, owner of Zara, as the world's largest clothing retailer. The great fast fashion war pits Sweden's richest man, Stefan Persson, chair of H&M, against Spain's richest man, Amancio Ortega, co-founder of Zara.

And now, in an audacious move, H&M is positioning itself as the ethical solution, the retailer that can make ethics and fast fashion synonymous. It wants to be an ethical giant, too. I say "audacious" because, to concerned consumers and activists, fast fashion's rapid-response production system, reliant on low-wage production in some of the poorest countries on Earth, is pretty much held responsible for environmental and social degradation in the global wardrobe. Indeed, having spent a large amount of time railing against it myself, it felt pretty audacious for me, too, to be sitting in the Stockholm headquarters of H&M last week.

The Observer was given early access to the brand's latest sustainability report that will be published on 12 April. Few corporate CSR reports are read so widely. From activists to analysts, everyone will be keen to see if H&M can really crack it. I am no different. However much I bang on about alternative ways to fill your wardrobe to ethically aware audiences – small brands, swapping, vintage, knitting – the top question I still get asked is: "So which high street stores can I go to?"

Be in no doubt, we are addicted to fast fashion. So, if H&M have solved all labour rights and environmental issues then I can pack up my soap box and toddle home, picking up some David Beckham underpants from his H&M Bodywear collaboration from one of the brand's 199 UK stores with total impunity. But how clean are H&M's Beckham pants? (On Twitter Joey Barton splendidly articulated lingering consumer unease: "Do one, Becks. They cost about 1p to make in a sweat shop in the Third World.") Indeed, what guarantees does H&M offer across its ranges?

"I don't think guarantee is the right word," says Helena Helmersson, head of sustainability, brightly. "A lot of people ask for guarantees: 'Can you guarantee labour conditions? Can you guarantee zero chemicals?' Of course we cannot when we're such a huge company operating in very challenging conditions. What I can say is that we do the very best we can with a lot of resources and a clear direction of what we're supposed to do. We're working really hard."

I believe her. Thursday's report will show some impressive sustainable figures: for example nearly 2.5 million pairs of shoes were made last year using lower-impact water-based solvents; all building contractors have signed a code of conduct to ensure "good" working conditions; recycled polyester equivalent to 9.2 million plastic bottles has been used, and H&M uses more organic cotton in production than any other group. This year I am told, 7.6% of its cotton was organic (an industry insider estimates H&M's overall cotton use to be around 200,000 tonnes a year). By 2020 100% will be sustainably sourced cotton.

"H&M has definitely got better," admits industry expert and CEO of Clothesource, Mike Flanagan. "From some presposterous moments in the recent past they have moved to being in a small clutch of four or five brands, including Nike and Gap, who believe that they have no alternative but to be as good as possible at sustainability. It's a marked change."

(The official word on the Beckham cruds is that this time they were made using conventional cotton and Elastane, but that H&M hasn't ruled out "using other [eco] materials for future collections" and didn't publish a list of factories used in China and Cambodia due to commercial confidentiality.)

Does Helmersson still wake up worried they'll be the subject of a sweated labour expose? "Yes, I worry about that sometimes. I lived in Dhaka for two years. You see how things happen down the chain in a country like Bangladesh. Remember that H&M does not own any factories itself. We are to some extent dependent on the suppliers — it is impossible to be in full control."

And therein lies the rub. While H&M talks about responsibility, in the supply chain where retailers devolve power to factories it can be easy to distance yourself. Helmersson says H&M has invested in 100 people in CSR, 75 of whom are auditors (assessing social and now some environmental conditions in factories) and produced a series of groundbreaking short films, including one on fire safety that it claims more than 400,000 garment workers have seen.

Sam Maher, of the NGO Labour Behind The Label, the UK platform for the international Clean Clothes Campaign, is not so impressed (although she is yet to see the latest 2011 report). "I'd like to be at the point where unions can phone H&M and talk through any labour disputes. The Clean Clothes Campaign should no longer need to exist. Sadly that's far from the case. DVDs 'educating' garment workers are all very well but I think workers know there is a problem. They aren't stupid. What's needed is proper dialogue with unions and freedom of association, long term investment and proper resources. It's not good enough to act unilaterally and say: 'We're Swedish and we do things very well.'"

What would change her mind? "For starters I would like to see them signing the Clean Clothes Campaign's memorandum of understanding on fire and building safety in Bangladesh. PVH [owners of Tommy Hilfiger] has just signed but three more big signatories are needed. H&M is currently considering it."

There is of course another fashionably attired elephant in the fitting room: a business model predicated on producing millions of units and on a fashion cycle that favours 30 to 50 trend-driven fashion seasons a year (the original spring/summer and autumn/winter cycles are alien to fast fashion) are hardly a recipe for sustainability. Isn't ethical fast fashion just a big fat oxymoron?

Helmersson says: "It's a question of how can we make the fashion more sustainable? That's what we are working on in many ways to do that."

To that end Thursday also sees the launch of the new Conscious Collection, with pieces made from eco-fibres ranging from organic cotton and recycled plastic bottles to Tencel (derived from plant cellulose) and a glamorous adjunct of "eco" pieces including a silky hemp, pieces that have been worn by celebrities on the red carpet (coincidentally this is a similar idea to the Green Carpet Challenge I co-founded with Livia Firth in order to up the profile of sustainable style).

H&M acknowledges there is more to do: "We must close the loop on fibre. How can we see waste as a resource?" emphasises Helmersson. "You see my dream is to be perceived as a company who can offer all people in the world – even those without much money – the possibility to dress really well and sustainably. That's how I want people to perceive us, not as a brand connected to mass consumption."

Full marks for ambition. But do I buy H&M as an ethical paragon? Not quite yet. They are still clinging to too many parts of the fast-fashion supply chain to bring anything revolutionary. But I'm enjoying their new attitude and I remain open to persuasion.