Amazon and Deliveroo are the subject of an in-depth probe by competition authorities into the e-commerce giant’s investment in the food delivery firm.
Neither company offered undertakings in response to concerns aired by the Competition and Markets Authority (CMA).
The CMA said earlier this month that the deal could cause higher prices and lower quality services for British consumers.
Announced in May, the deal gave Amazon a stake in Deliveroo of just over one-sixth.
The US online retailer was the lead investor in a $575m (£442m) funding round.
Deliveroo hoped the deal would give it an edge over rivals like Uber Eats and Just Eat.
But the CMA has now referred the deal to a full investigation, casting doubt on whether the investment will be allowed to happen.
The regulator could block the deal altogether, or demand remedies and assurances from both sides.
It said the investigation would have a deadline of 11 June next year.
One of the biggest worries was how the deal could affect the nascent ultra-fast grocery delivery market.
Deliveroo has been making deliveries for Morrisons and the Co-op, while Amazon offers a one-hour service for customers with Prime subscriptions.
The sector remains small, but the CMA is concerned the merger could hit competition.
A Deliveroo spokesperson said: “Deliveroo has been working closely with the CMA and will continue to do so.
“We are confident that we will persuade the CMA of the facts that this minority investment will add to competition, helping restaurants to grow their businesses, creating more work for riders, and increasing choice for customers.
“Deliveroo is a British company operating right across the country and this investment will be particularly beneficial to the UK economy.”
An Amazon spokesperson added: “A homegrown UK business like Deliveroo should have broad access to investors and supporters.
“Amazon believes that this investment funding will lead to more pro-consumer innovation by helping Deliveroo continue to build its world-class service and remain competitive in the restaurant food delivery space by creating more highly skilled jobs, innovating in the restaurant food delivery sector, and developing new products for customers.”