The 1.5 billion pound Ocado Retail venture is a cornerstone of M&S's latest attempt to turn itself around and offset problems at its pandemic-hit clothing business.
"The M&S launch has been incredibly popular. We have seen a surge in demand for M&S products in the run up to launch which has impacted a very small number of orders today," said an Ocado spokeswoman.
"The vast majority of customers are unaffected and will be delivered as normal. We would like to thank our customers for giving M&S such a big welcome and sincere apologies to any customers having to wait a bit longer."
After a decade of failed revamps and amid plunging sales in clothing and homewares, M&S could have done with a flawless launch.
Shares in M&S were down 4.4% at 1207 GMT, extending 2020 losses to 50%. Ocado shares, which have nearly doubled this year, were up 0.6%.
The venture ends Ocado's two-decade supply contract with supermarket chain Waitrose, part of the employee-owned John Lewis Partnership [JLPLC.UL], and replaces some 4,500 Waitrose products with the full M&S food range of 6,000 products and 800 everyday clothing and home lines.
Online grocery shopping has doubled its share of the UK market to 14% since the start of the COVID-19 pandemic, and Ocado reckons it could reach 30% over the next few years.
Waitrose sees the split with Ocado as an opportunity to further develop its own online services.
"You can count this as our graduation day, we're ready to go on our own," Waitrose Executive Director James Bailey told Sky News.
"We've got 160,000 order slots ready for our customers, they're full every week and we're growing week on week, so we're pretty confident about the future," he said.
On Friday Waitrose said it was teaming up with Deliveroo to trial fast home-delivery.
(Reporting by James Davey; Editing by Alistair Smout, Kate Holton and Susan Fenton)