British Airways and Virgin Atlantic have criticised a new "open skies" deal between the European Union and US that aims to open up their airline markets.
British Airways has endured a number of difficult years
British Airways said the deal was not good for UK aviation, while Virgin called it a missed opportunity.
On Friday and after years of failed talks, the EU and US said that they had made decisive progress and managed to get the outline of a new agreement.
The transatlantic airline market is worth some $18bn (£9.3bn).
According to the EU, a new deal would boost transatlantic passenger numbers by 26 million, create 80,000 jobs, and provide 12bn euros (£8.1bn) of economic benefits.
The worry for many critics is that the deal favours US carriers, and that companies such as British Airways and Virgin would face more competition on prized routes to and from Heathrow airport.
British Airways said it would be looking to lobby on the issue and would put forward its point of view that the deal "is not good for UK aviation".
Steve Ridgway, the chief executive of Virgin Atlantic, said: "We would love to see full and proper open skies but this draft agreement doesn't come near that."
The open skies deal has proved difficult to finalise
"This appears at first glance to be a missed opportunity to create a truly competitive transatlantic aviation market," he added.
However, the UK's Independent newspaper quoted rival airline BMI as saying that the "open skies" agreement was a "major breakthrough".
BMI has been lobbying for more access to Heathrow, and called on the UK government to support the draft proposal, the Independent reported.
EU ministers will have to vote on the deal on 22 March. Should they approve the deal then it would be in place from 28 October.
As part of the deal, European airlines would be allowed to make transatlantic flights from any nation and not just their home country.
It would also open up Heathrow so that a greater number of airlines could land and take off from the London airport.
Ownership rights, which had proved controversial in earlier rounds of talks, would also be fine-tuned.
The US would still be able to prevent a foreign company from owning more than 25% of an American airline's voting rights.
However, the deal would make it easier for EU companies to buy all of an airline's non-voting shares. At the same time, the EU would be able to restrict US investment in EU airlines.