Airlines are baulking at increased charges being proposed as part of a £3 billion five-year development plan for Heathrow.
Virgin Atlantic described the planned price rise as "incredibly steep" and British Airways said it hoped any final decision would not "penalise customers".
Charges - which need to be approved by the Civil Aviation Authority - will rise by the equivalent of £19.33 per passenger for 2012-13 up to a possible £27.30 in 2018-19 under the proposals.
The regulator will now develop and consult on its own proposals before coming to a final decision on airport charges in January 2014.
The plan is separate from any decision on whether a third Heathrow runway is built. The Davies Commission into UK airport capacity is not due to publish a final report until summer 2015.
Virgin Atlantic said: "We are totally committed to improving the passenger experience at Heathrow.
"However, we believe this can be done without a repeat of the incredibly steep price rises we have seen in airport charges in the last few years.
BA said: "We hope the regulator will give a fair ruling in the months ahead, which doesn't penalise customers and airlines."
Heathrow said the increased charges would pay for investment including the opening of the new Terminal 2 in 2014, improved check-in and baggage facilities and better surface access.
The airport’s owners plan to upgrade stands and taxiways that will help to make Heathrow the busiest hub in Europe for A380 superjumbos.
“Following the introduction in 2011 of new incentives and penalties to encourage airlines to operate the quietest aircraft, we will continue to trial new operational procedures that can reduce noise for local communities and roll out improved noise insulation schemes for local properties,” Heathrow said.
“We believe Heathrow’s plans represent good value for passengers, airlines and the UK as a whole.
“Our investment will deliver a better journey for passengers, more efficient and reliable infrastructure for airlines, and additional jobs, trade and economic activity for the UK.”
Heathrow chief executive Colin Matthews said: ““Heathrow is the UK’s only hub airport and a strategically important national infrastructure asset.
“Heathrow faces stiff competition from other European hubs and we must continue to improve the service we offers passengers and airlines.
“We have invested billions of pounds in new facilities such as Terminal 5 in recent years and passengers say they have noticed the difference.
“Our plan for a further £3 billion of private-sector investment will further improve the airport for passengers. The plan represents good value for money for airlines and passengers and comes at no cost to taxpayers.”
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