With Shein specialising in delivering clothes to your door, Primark does offer click-and-collect services in its nearly 200 UK stores - but not deliveries.
Some high-street retailers have been struggling in the UK, but Primark has largely bucked the trend - it's closing a store in Dartford, Kent, next year, which reports say will be its first store closure in a decade. It also opened dedicated Primark Home stores in Belfast and Manchester.
Primark relies on its customers shopping in bulk, Mr Stevenson says. "You might be going in for one thing, but you end up buying seven things that you hadn't really thought about," he says. This doesn't happen as much with online shopping, he says.
Would Primark's sales be boosted if it did offer delivery? Mr Stevenson is sceptical, saying "it doesn't feel like they're losing out by not doing that", but that it could be an option in future.
"If you wanted to buy a couple of things from Primark for £5 each, are you going to pay 50% of that in delivery charge?" he asks. "Because buying £10 of stuff is going to cost me £5 to get it tomorrow."
Primark's spokesperson said that its online model was a "deliberate choice to streamline operations and pass the savings directly to customers".