The Competition Commission also recommended that Spanish-owned BAA lose control of either Edinburgh or Glasgow airport.
In a preliminary report, the CC said there were competition problems at each of BAA's seven UK airports "with adverse consequences for passengers and airlines".
The CC report - with a final report on BAA's airport ownership due at the end of the year - effectively means that BAA will have to give up running Gatwick and Stansted as the commission made it clear that it was "unlikely to require the divestiture of Heathrow unless the sale of Gatwick or Stansted is likely to be impractical or ineffective".
BAA also runs Southampton and Aberdeen airports.
The commission was also critical of Government aviation policy, saying "aspects of Government policy restrict or distort competition by contributing to the current capacity constraints at BAA's London airports".
BAA chief executive Colin Matthews said: "By calling not just for a fundamental restructure of BAA but also for a review of the Government's air transport White Paper, the commission risks delaying the delivery of new runways and making better customer service less, not more, likely."
The CC said as well as now consulting to see which airports need to be sold, it was also seeking views on the need for "some form of enhanced regulation at Heathrow.
The CC said that it believed that "separate owners would be more active than BAA in exploiting existing opportunities" at south east England airports.
The commission also said there were competition problems arising from the existing planning system and the system of regulation for airports which is under the control of the Civil Aviation Authority.
The commission said it did not expect to require the sale of either Southampton or Aberdeen airports.
Christopher Clarke, chairman of the CC's BAA airports inquiry group,
said: "We have provisionally found that there are significant competition problems arising from BAA's common ownership of seven UK airports.
"This is evident from a large number of factors including its lack of responsiveness to the needs of its airline customers and a lack of initiative in planning capacity.
"This has resulted in investment that is not tailored to the requirements of airport users and lower levels and quality of service for both airlines and passengers."
He went on: "We have also provisionally found that there are competition problems arising from the planning system, aspects of Government policy and the system of regulation."
"While we accept that constraints on runway capacity in the south east will limit the scope for the benefits of competition in the short-term, we believe that separate owners would be more active than BAA in exploiting existing opportunities.
"Over time, we would expect these to increase significantly. In Scotland, where there are no similar capacity constraints, we believe separate owners of Edinburgh and Glasgow would similarly improve their offerings. BAA has argued to us that there is no scope for competition to develop so long as there are capacity constraints. We take the opposite view.
"Unless the market is opened up to competition, there is a serious risk that the current capacity constraints will persist, certainly for longer than in a better functioning market."
Mr Clarke said there was a serious shortage of capacity, particularly runway capacity, in south east England.
He went on: "The earliest new runway capacity will become available is 2015 at Stansted with no additional runway capacity possible at Heathrow before 2020.
"While we accept that Government policy and the planning regime have contributed to the lack of capacity, we have found that BAA as the owner and operator of these London airports has played a major role in not pressing for more capacity sooner and in planning terminal and runway capacity on a conservative and sequential process such that its plans for one airport have been influenced by its plans elsewhere. We accept, however, that BAA has been more successful in undertaking several smaller projects simultaneously."
"In Scotland, BAA has until recently been noticeably slow to develop new routes at Glasgow and Edinburgh, while at Aberdeen, its investment plans are regarded as unambitious despite relatively high levels of profitability. At Southampton, it has shown a reluctance to respond to its customers' demands."
A number of companies have already expressed interest in taking over the running of any BAA airports that could come up for sale, including the Manchester Airports Group, which operates Manchester, Humberside, East Midlands and Bournemouth airports.