Forever 21, H&M and Zara have been rapidly gobbling up more space and shopping dollars in American malls as teens and millennials flock to their stores full of uber-trendy clothes at rock-bottom prices.

Now, these fast-fashion mainstays are about to get fresh competition in the United States from a chain that already gives them a run for their money in Europe.

Primark — a retailer that was founded in Ireland and is currently owned by a British company — plans to make the leap across the pond in September with its lineup of $3.50 T-shirts, $10 jeans and $5 ballet flats.  As it opens its first store in Boston on Sept. 10 and then fans out with seven more outposts across the Northeast, Primark’s arrival will serve as something of test of whether our appetite for wear-it-today, trash-it-tomorrow clothing is anywhere near satiated.

Primark is sometimes described as the overseas answer to Forever 21: Its stores quickly sell through high volumes of merchandise, meaning the sales floor is constantly updated with new clothes. And its hyper-efficient supply chain has allowed it to quickly crank out of-the-moment pieces. In the U.K., this has earned it the nickname “Primarni,” a mash-up of Primark and Armani.

Rob Gregory, global research director for London-based consultancy Planet Retail, said that Primark has been one of the lone bright spots lately in a subdued U.K. apparel market. Indeed, in the most recent quarter, its sales were up an eye-popping 12 percent.

“Traditionally there’s been a bit of a stigma of buying cheap clothes,” Gregory said. “But over the past five years, to go to Primark and buy a cheap dress or shirt is actually sort of a badge of honor.”

In some ways, it seems like an apt moment for Primark to arrive on U.S. shores: Consumers remain intensely value-conscious, and teen shoppers have nearly dealt death blows to once-formidable retailers who haven’t adapted quickly to trends that bubble up on Instagram and street style blogs. And yet some retailers and experts are questioning whether we might soon see a return to wardrobes filled with classic investment pieces.  (The success of Everlane, purveyor of long-lasting basics, could be a sign of such a pendulum shift). Plus, the fast-fashion market here is already quite crowded.

“It’s really a saturated environment,” said Tiffany Hogan, a London-based apparel analyst for Kantar Retail.  

Today, Primark has 287 stores across the United Kingdom, Ireland and several countries in continental Europe. The retailer is beginning its foray into the United States with stores in the Northeast, based on their belief that tastes in that region will be most similar to those of its European customers.  

“Many retailers have found that coming from Europe to the Northeast has been a much easier leap to make,” Hogan said.

In addition to the Boston store, Primark plans to soon come to locations such as Danbury, Conn.; Staten Island, N.Y.; and at the sprawling, upscale shopping mall in King of Prussia, Pa.

“We deliberately located these first stores in locations where there’s a high footfall already, because we are aware that the consumer awareness of Primark is low,” said John Bason, chief financial officer of Associated British Foods, the company that owns Primark.

One of Primark’s key challenges will be differentiating itself not only from fellow fast-fashion operators, but also from other value-focused apparel retailers such as Target, Old Navy and TJMaxx. Bason hopes that the vibe of the stores will help with that. He’s promising Primark’s U.S. outposts will be bright, vibrant and “not a miserable experience, like some other value retailers.”

Bason also adds that Primark’s goal isn’t necessarily to make customers abandon their current value-priced favorites.

“I think that our customers don’t mono-brand shop,” Bason said. “They’re looking for a repertoire of which we want Primark to be one of those stores.”

Primark found spaces for its stores in the United States in an unusual way: It has signed lease agreements to take over parts of existing Sears stores.  The Primark stores will not be “store-within-a-store” concepts; they will be standalone stores with separate entrances and branding.  Bason said these deals were attractive to Primark because it allowed them to get access to spaces of more than 70,000 square feet, a large footprint that might otherwise have been hard to nab in a U.S. shopping center.  Sears, meanwhile, has said the deals allow it to use otherwise unproductive real estate to generate some income.

Primark’s owner, Associated British Foods, is an international conglomerate that includes one of the world’s largest sugar producers, an agricultural supplier and grocery store brands such as Ovaltine. The Primark name is used in the U.K. and at its stores throughout Europe, but its stores in Ireland are branded as Penneys.

Even as it arrives in U.S. malls, Primark won’t be making a play for your online shopping business. The retailer has opted not to have an e-commerce site, as it believes its low-margin, high-volume sales model is not well-suited to selling in that channel.

“This is not a profitable avenue for us,” Bason said.