The airline said the suspension will also impact some long-haul flights depending on the date and route.
Fares are still available to book on BA flights arriving into Heathrow.
The airline said the move came in response to Heathrow’s request to limit new bookings after last month introducing a passenger cap of 100,000 people on departing flights until September 11.
To meet the cap, BA announced it would cancel 10,300 flights until October, with one million passengers affected.
The airline is now limiting the number of seats it is selling on each flight to ensure it stays under the limit.
BA said the move will protect existing bookings because there will be more seats available for customers who miss connecting flights due to disruptions such as air control restrictions or weather issues.
In a statement, the airline said: “We took pre-emptive action to reduce our schedule this summer to give customers certainty about their travel plans and to build more resilience into our operation given the ongoing challenges facing the entire aviation industry.
“When Heathrow introduced its passenger cap, we took a small number of additional flights from our schedule and to continue to comply with the cap, we’ve been taking responsible action by limiting sales or all the available fares on some of our Heathrow services to ensure more seats are available to rebook customers.
Although this move by BA will allow it more flexibility to rebook passengers in the event of further cancellations or disruption, it reduces consumer choice and will lead to significant price increases
Guy Hobbs, Which? Travel
“We’ll continue to manage bookings to be within the Heathrow imposed cap so we can get our customers away as planned this summer.”
However, the airline has been criticised over the decision amid concerns it could push up prices for flights with other carriers.
In recent months, many passengers flying to and from the UK’s busiest airport have suffered severe disruption, with long security queues and baggage system breakdowns.
Meanwhile, tens of thousands of flights have been cancelled to cope with the demand for air travel amid staffing shortages.
Guy Hobbs, editor of Which? Travel, said: “Following months of delays and last-minute flight cancellations that have caused misery for thousands of travellers, passengers now face this drastic, last-minute decision from British Airways to suspend flight sales.
“Although this move by BA will allow it more flexibility to rebook passengers in the event of further cancellations or disruption, it reduces consumer choice and will lead to significant price increases.
“With further ticket sale suspensions possible, people should consider booking as early as possible to avoid last-minute disappointment and inflated fares. They should also consider alternative airports and airlines where possible.
“Airports and airlines need to be held to account for the unacceptable disruption travellers are currently experiencing, and the Government must act to ensure the Civil Aviation Authority has the power to hit operators with substantial fines in instances where they flout the rules.”
Last month, Emirates rejected Heathrow’s order to cancel flights to comply with the cap.
The airline accused the airport of showing “blatant disregard for consumers” by attempting to force it to “deny seats to tens of thousands of travellers” through the cap.
A Heathrow spokeswoman said at the time it would be “disappointing” if “any airline would want to put profit ahead of a safe and reliable passenger journey”.
Virgin Atlantic also criticised the airport’s actions and claimed it was responsible for failures which are contributing to the chaos.
— Competition & Markets Authority (@CMAgovUK) July 21, 2022
Airlines on July 21 were accused of “harmful practices” in their treatment of passengers affected by disruption.
The Competition and Markets Authority and the Civil Aviation Authority issued a joint letter to carriers, expressing concern that “consumers could experience significant harm unless airlines meet their obligations”.
The letter said: “We are concerned that some airlines may not be doing everything they could to avoid engaging in one or more harmful practices.”
These included selling more tickets for flights “than they can reasonably expect to supply”, not always “fully satisfying obligations” to offer flights on alternative airlines to passengers affected by cancellations, and failing to give consumers “sufficiently clear and upfront information about their rights”.