Steve Rowe announced that the move would allow shoppers to order school uniforms, lingerie or evening dresses online to be picked and delivered from M&S stores.
Asos and Next offer next-day deliveries, while fashion chain Zara offers same-day deliveries to customers based in London only, for twice the standard delivery charge.
M&S is understood to be offering a same-day service nationwide.
The retail boss told The Times it emphasises how traditional retailers with bricks and mortar stores could adapt to the shift to online commerce, instead of blaming the Internet for the decline of the high street.
He said the move puts M&S in a position where the big retailer has a “multichannel proposition so we can be where our customers want and they can choose how quickly they want it”.
M&S has around 1,000 physical stores, with just over 250 selling clothing, home and food ranges.
Earlier this year, the retailer plunged to a £201m loss due to the coronavirus lockdown and said it will close 100 stores as it moves high street shops to retail parks.
But Rowe said the retailer’s strategy to sell brands from other companies on its website was proving to be a draw for customers, pointing towards 14 per cent of customers who bought a dress from sustainable brand Nobody’s Child, a brand newly added to M&S womenswear.
The strategy, which launched in October, aims to have 40 third-party brands listed on M&S by the end of 2021. These include Smiggle, Joules, Triumph and Havaianas.
Rowe said this was helping the retailer increase its market share in its key categories, but resisted suggestions that M&S was turning into a department store.
He told The Times that the reason John Lewis, Debenhams and House of Fraser had struggled was because they were too similar, adding that people wouldn’t know which department store they were in if they were blindfolded outside each one.
“Their only differentiator is price and service,” he said. “We are putting a curated range of brands together, not hundreds of brands. We’re also giving the brands access to 39 million customers.”
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