While the deal was secured earlier this year, Britons have only been able to order M&S products from today.
However, some shoppers have already been left disappointed as some orders have been cancelled.
Many took to Twitter to share their frustration after they were unable to get the items they wanted.
One Twitter user said: “Not the best start for the @Ocado and @marksandspencer partnership when an order for 9am on launch day has things missing from it – it’s not like you’ve sold out of the stuff is it?”
“@ocado delivery for Thursday has been cancelled! Was rather looking forward to the Percy Pigs we had ordered,” another added.
A third quipped: “@Ocado Online queues and no delivery slots for a week, are we going into another lockdown?”
One user wrote: “@Ocado cancelled todays 7:30am delivery, at 22:30 last night.
“First day delivery @marksandspencer it’s already a disaster!”
“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.”
Ocado previously had a deal with Waitrose and had delivered goods from the supermarket for 20 years.
This has now been replaced with the partnership with Marks & Spencer.