Primark's website crashed on Monday, shortly after the retailer finally launched its click-and-collect service.
It is starting a trial in 25 stores in north-west England, Yorkshire, and north Wales for children's products only.
The budget chain, which lost more than £1bn in sales during the pandemic when its stores had to close, has succumbed to the online shopping revolution but it is not planning deliveries.
Primark said it was aware some people had issues accessing its site.
"We're working hard to address this to ensure that everyone can access and browse the site easily," the company said in a statement.
By mid-afternoon, the website appeared to be back up and running for some customers.
Paul Marchant, the retailer's chief executive, said the launch of Primark's click-and-collect service was a "milestone for us and a really important moment".
"We're massive fans of bricks and mortar. We believe in stores and we believe in the High Street. We think click-and-collect is the right proposition," he told the BBC in a rare broadcast interview.
The retailer is hoping that giving customers the chance to shop online and then pick up in-store will drive more customers to its shops.
'Well set for Christmas'
During the pandemic lockdowns Primark's 190 UK stores were forced to close their doors, and it had no online operation to fall back on.
But Mr. Marchant says the High Street now seems buoyant again.
"We feel excited about Christmas. I think we're well set. Our stores are feeling busy.
"It's the first time in three years that customers have been able to come into the store, mask-free, restriction-free, and enjoy the experience of being in a Primark store."
Last week Primark's parent group, ABF, said it would freeze prices for Primark's clothes beyond what was already planned for this winter, despite rising costs.
As the cost-of-living crisis bites, people have been looking to save money where they can. Supermarkets have seen shoppers swapping out brands for cheaper, own-label products, while many people have been stocking up on warm clothes to save money on heating.
Primark itself says its snuddie, or an oversized hoodie, has been one of its bestsellers so far this winter.
The retailer has defied the wider gloom on the High Street and Mr. Marchant says it has picked up new customers because of the cost-of-living crisis.
"I think customers are looking for better value all the time. I think at Primark, we offer them outstanding value. And I think we are attracting new customers as a consequence of that."
The new department store?
Primark has also been upping its game at its biggest "destination" stores, like its vast Manchester city center one, with cafes, a barber shop, a vintage concession store, and pop-up space to personalize Primark products.
"We are, I think, the new department store because I think we offer something for everybody but done in a new and exciting way," Mr. Marchant says.
And this now includes dipping its toe into the world of e-commerce.
Retail analyst Catherine Shuttleworth, CEO, and founder of Savvy Marketing says Primark is simply bowing to the inevitable.
"They've had massive highly successful physical store growth, not just in the UK and Ireland, but also across the world. However, that dependency on a store-only format has its limitations as Primark found out to their cost in the retail lockdowns during the pandemic," she says.
An online presence not only allows them to reach shoppers who can't easily access a store, or don't have time to queue up so want flexibility in when and where they visit, she says click-and-collect may also become important for the hordes of Primark fans to get their hands on products quickly before they sell out.
Given the costs of fulfilling and delivering online orders, and dealing with high levels of returns, it can be hard for retailers to make the economics of e-commerce stack up.
"Online is a huge commercial undertaking and the logistics for a business with the size and scale of Primark are enormous. Click-and-collect is the most sensible way to run this operation, not least because it allows returns to be placed back into the store stock to help keep costs down," Ms. Shuttleworth says.
