Heathrow could be forced to allow other companies to design and build its third runway and new terminal after the UK aviation regulator argued that rival bids could keep construction costs down.

A long-awaited review by the Civil Aviation Authority (CAA) proposes changes to the regulatory model that governs how Heathrow runs and covers its costs.

These include making the operator seek bids from other businesses to design, build and operate parts of the long-delayed expansion project at Europe’s busiest airport, which it said “would allow for direct competition between Heathrow and an alternative developer … [that] could encourage competition and efficiency”.

The CAA’s most radical suggestion, which would require special approval from the government, would allow another developer to tender to build and run their own terminals at Heathrow, similar to a scheme at JFK airport in New York.

Last November ministers backed Heathrow’s plan for the runway to be up and running by 2035, over the rival proposal submitted by Arora Group, although the airport operator is still seeking formal planning approval to start construction by 2029.

Earlier this month it emerged that Philip Jansen, Heathrow’s new chair, had moved to open talks with airlines and Arora Group’s chair, Surinder Arora, to attempt to progress plans to expand the airport amid a row over how much the scheme would end up costing carriers, retailers and, ultimately, passengers.

British Airways dominates Heathrow, accounting for more than 50% of slots, and Luis Gallego, the chief executive of BA’s owner, International Airlines Group, has said the cost of the third runway and associated works must be capped at £30bn.

Heathrow is considered to be Europe’s most expensive airport, and in March the UK aviation regulator rejected its plans to significantly raise its landing fees to fund a multibillion-pound upgrade.

Arora has been promoting his own £25bn expansion scheme and is part of Heathrow Reimagined, which also includes BA and Virgin, which is campaigning to drastically reduce the costs of operating at the airport.

“Two years ago competition at Heathrow wasn’t on the cards and now is very much alive and kicking because the case for change is so strong,” said Arora, the founder of Arora Group. “We welcome this consultation from the CAA.”

The CAA said there could be difficulties in implementing a model allowing rival bidders. “This model could encourage competition and efficiency,” the regulator said. “Nonetheless, there would also be some complications in implementing such a model.

“It would be important to ensure that an approach involving the build, operation, ownership of assets and direct competition with Heathrow worked in a way to further the interests of consumers across the whole airport.”

Heathrow, however, warned that the proposals could “undermine efforts” to expand the airport and produce growth.

A Heathrow spokesperson said: “Economic growth is key to tackling the cost of living crisis. We have a clear plan to invest billions of pounds of private capital to upgrade and expand the UK’s hub airport – creating jobs and growth across the country.“We support reform that boosts efficiency, cuts red tape and keeps investment flowing, but not proposals which will undermine our efforts to improve the airport for consumers or delay the economic growth the country needs. We look forward to working with government and the regulator to turn these proposals into positive outcomes.”

Heathrow is owned by a consortium of investors led by the French company Ardian and includes the sovereign wealth funds of Qatar, Singapore and Saudi Arabia.