One shopper has come from Denmark and spent over £1,000. Grans, mums and schoolmates are all filling baskets with T-shirts, sequinned trousers and pyjamas. This is Primark, the cut-price fashion chain that has grown from one shop in Dublin in 1969 to become the UK’s biggest seller of clothing, offering everything from pants and socks to headphones and party dresses.

It already sells more items of clothing than any other retailer, and this year it is expected to overtake Marks & Spencer to become the biggest clothing retailer by value, too. While M&S is rapidly losing sales and closing shops, Primark is expected to account for £1 out of every £14 spent on clothing in the UK this year, according to market analysts GlobalData.

Primark opened four new UK stores this year, including its biggest yet, a 14,800 sq metre giant in Birmingham. These five floors of fashion, a Disney cafe and Harry Potter shop have become a coach-trip destination akin to the Blackpool illuminations – and can even pull in shoppers from abroad, like the Danish woman who makes an annual pilgrimage especially to shop at Primark.

The Primark Disney Cafe at the Birmingham shop. Photograph: Aaron Chown/PA

And it is doing all this during a dire year for the British high street, in which a string of names have gone bust, including Karen Millen, Bonmarché, Jack Wills and LK Bennett. House of Fraser and Debenhams are both expected to close numerous stores as their owners struggle to stay afloat, and last week the UK business of Mothercare collapsed into administration.

Sales at Primark’s established stores slipped by 1% in the year to 14 September, but that looks insignificant compared with diving sales elsewhere, including a 5.5% fall in like-for-like sales revealed last week by Marks & Spencer.

Many high street retailers blame their woes on the rise of the internet, but Primark is thriving without an online store or home deliveries. It plans to open 19 more stores in the UK and Europe in the next 12 months, including one in a former Bhs at Manchester’s Trafford Centre. It is also stepping up expansion in the US, partly making use of space abandoned by failed department stores such as Sears.

Low prices seem to be a key part of the magic. At the Birmingham store, it is possible to buy a bra for less than £2, kids’ Christmas pyjamas for £5 and a multitude of dresses for £10. That compares with a minimum of £8 each for a two-pack of bras at M&S and or £5 each in a two-pack at Debenhams.

Shoppers cite low prices as the biggest draw. “My kids call me Primark Queen,” says Jane Biddle, 44, standing outside the store surrounded by brown paper bags of tops, dressing gowns and other Christmassy items after spending two hours in the store. “It’s all in there: they’ve got what you want,” she said. “You can save quite a lot of money but you could spend a bomb because the value is so good.”

YouTuber Saffron Barker, pictured with fans, has had exclusive collections at Primark. Photograph: Jeff Spicer/Getty Images

Lucy Farrington, 19, and her sister Olivia – out shopping with their mum and dad – say they’re fans of young fashion websites such as Pretty Little Thing, Missguided and Asos, but like Primark “because it is cheap and convenient. Everything is in there, from clothes to chargers and makeup.”

Restricting itself to a relatively small number of stores – 189 in the UK compared with about 300 clothing outlets for Marks & Spencer and more than 400 for New Look – helps Primark operate more efficiently and keep prices low.

James Clark, a lecturer at the London College of Fashion, says the combination of relatively large, well-appointed shops and low prices also means it becomes a go-to destination in each local area. The more recent additions of cafes, nail bars and hair salons also help it stand out.

“It’s a category killer approach,” says Clark. “They dominate a local market, while the likes of M&S or Next are just one of a number of similar stores.”

John Bason, finance director of Primark’s parent group, Associated British Foods – which is controlled by the billionaire Weston family – says selling online would only add costs and undermine the low prices.

“I can’t tell you how much cost is added by picking and individually packing those items [to sell online],” he says. “If you are talking about the essentials [such as underwear or T-shirts] we have a very, very efficient way of getting it to the customer.”

Primark also spurns traditional advertising, instead using social media to connect with young shoppers and entice them into stores.

Primark hopes to avoid M&S's fate – alienating young people who don't want to shop where their grandparents did – by keeping on top of new trends

The brand has 20 million followers on sites such as Instagram, Facebook and Pinterest, up from 13 million last year. Primark creates a buzz through links with influencers and celebrities and via the Primania social site, where fans post pictures of themselves in Primark outfits – often with the price tag attached.

It also taps into online trends with the shopping equivalent of clickbait. This week, the Birmingham store showcased cheap gifts linked to Disney’s Frozen franchise, PlayStation and Call of Duty, as well as Funko collectible dolls.

Bason credits Primark boss Paul Marchant, a former New Look executive who took the helm in 2009, for its continuing growth.

“Amazing prices is where it all started, but the thing that propelled us is the magic of Paul Marchant and what he has done with fashionability, constant surprise and newness,” he says. “About 50% of what we sell is basics, but there is a lot of new stuff and fun things coming into stores all the time.”

He says keeping on top of trends will help save Primark from M&S’s fate: going from being the family favourite to alienating younger shoppers who didn’t want to shop where their grandparents did.

If there is one problem on the horizon, it is the threat of a backlash against its cut-price model, which seems out of tune with the youth environmental movement fronted by Greta Thunberg.

The chain’s fast fashions have been criticised for fuelling unsustainable throwaway culture as well as low wages at its overseas suppliers.

Chloe Collins, analyst at GlobalData, thinks this could become a problem for Primark: “Fast fashion has been a big thing but people are becoming more aware of sustainability.”

Primark is responding with a sustainable cotton initiative, training more than 160,000 independent farmers to use less pesticide, fertiliser and water. It says it has already sold 14 million pairs of pyjamas, 3 million pairs of jeans and 6 million duvet covers and towels made with this cotton. It is also testing out recycled polyester fabric and a clothing recycling scheme that could be extended across the chain next year.

Bason says Primark is now seen as a leader on ethical sourcing, after it dramatically increased its global factory monitoring teams. This was in response to a 2009 scandal over underpaid factory workers at one supplier in the UK and the 2013 Rana Plaza disaster in Bangladesh, where more than 1,000 people died at a factory complex making clothes for Primark and a number of other brands.

Aside from efficient systems and avoiding home delivery, Bason insists that Primark’s low prices are the result of volume discounts from suppliers, and lower profit margins on each item. “Our suppliers sell to all the major brands on the high street,” he says, “and I know the price we buy at is not that different.”

A memorial to those who died in the Rana Plaza collapse on the outskirts of Dhaka, Bangladesh. Photograph: Getty Images

In 2008, the group had only a handful of people overseeing conditions at the factories it uses – now it has more than 100. Dominique Muller of campaign group Labour Behind the Label says: “Primark is now much more rigorous in terms of knowing and monitoring its supply chain.” She says it also publishes a list of its “tier one” clothing manufacturers – in line with best practice in the industry – so campaigners can monitor conditions at its factories.

Clark, however, says Primark needs to build sustainability into the whole business, not just a few pairs of sustainable jeans, if it is to satisfy young people’s growing interest in ethical issues: “More and more people are becoming socially aware. That poses questions for the future.”