A multimillion-pound investment by Amazon in the UK takeaway delivery firm Deliveroo could leave customers, restaurants and grocers facing higher prices and lower quality services, British regulators have said.

The two companies have five days to come up with proposals to counter concerns raised by the Competition and Markets Authority or potentially face an in-depth investigation that could take six months.

Amazon could ultimately be forced to sell or reduce its stake in Deliveroo in order to gain approval from the regulator. In previous similar cases which resulted in years of legal wrangling, broadcaster BSkyB was forced to sell more than half its 17.9% stake in ITV, while Ryanair was ordered to slash its near 30% stake in rival Aer Lingus.

The CMA began its investigation into the Deliveroo deal after Amazon revealed in May that it was the lead investor in a $575m (£452m) funding round for the takeaway tech firm, giving it a 16% stake in the London-based business.

The deal sent shockwaves through the food delivery sector as investors anticipated the US technology giant would use its financial muscle to take business from rivals such as UberEats and Just Eat.

While Amazon has stressed it has only a minority stake in Deliveroo, the CMA said it was concerned that competition could be damaged because Amazon might be discouraged from re-entering the food delivery market, which it exited last year.

The competition watchdog also raised concerns that a tie-up between Amazon and Deliveroo would dampen competition in the ultra-fast grocery delivery market in the UK, in which there were currently only a small number of suppliers. Deliveroo has been testing out sub-two hour deliveries for Morrisons and the Co-op while Amazon offers a within-the-hour service to its Prime subscribers in some areas. They are up against other express services including Sainsbury’s Chop Chop, the Co-op’s own e-bikes, Ocado Zoom and Waitrose’s Rapid delivery service.

The regulator said that the two companies were among the strongest players in the nascent ultra-fast grocery market, as they both have UK-wide delivery networks. It said that, if they remained separate, competition between the two companies could increase, to the benefit of customers.

Andrea Gomes da Silva, the CMA’s executive director, said: “If the deal were to proceed in its current form, there’s a real risk that it could leave customers, restaurants and grocers facing higher prices and lower-quality services as these markets develop.

“This is because the significant competition which could otherwise exist between Amazon and Deliveroo would be reduced.”

Deliveroo said it had been working closely with the CMA and would 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,” it said.

In May, Deliveroo said it would use money from the Amazon-backed funding round to invest in its technology team at its London headquarters and to further expand its geographic reach and open more of its delivery-only kitchens.

An Amazon spokesperson said: “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.”

The company, founded by the former banker Will Shu in 2013, reported a loss of £232m last year despite a 72% rise in sales to £476m. Having started in London, it now operates in 500 towns and cities across 13 markets worldwide, including Australia, Belgium, France, Hong Kong, Italy, Ireland, the Netherlands, Singapore, Spain and the United Arab Emirates.