The Cenotaph in London will not be shown on Top Gear footage filmed over the weekend, the BBC says.
The show has been criticised after host Matt LeBlanc and a professional driver performed "doughnuts" near the war memorial.
Co-host Chris Evans apologised for the stunt, and said he and the crew were "mortified".
In a statement, the BBC apologised and said the Cenotaph was never intended to appear in the programme.
It also said it had consulted with the Metropolitan Police film unit and the special events unit of Westminster City Council over the "large-scale, complex shoot, prepared over a period of four months".
This, the corporation said, "required numerous road closures, health and safety regulations to be in place, and also included full disclosure to local residents, including the Treasury and Foreign Office".
It added: "The Cenotaph was at no point intended to feature in the programme and therefore will not appear in the final film.
"However, we are acutely aware of how some of the images in the press look today via the angle and distance they were taken and for which, as Chris Evans has already said, we sincerely apologise.
"The driver of the car was briefed by production prior to filming as to where to drive and to not do any manoeuvres close to the monument, an instruction to which he fully adhered.
"We would like to make it absolutely clear that the Top Gear team has the utmost respect for the Cenotaph, what it stands for, and those heroic individuals whose memory it serves so fittingly."
During an interview given on Monday morning, Evans had said: "That footage will definitely not go on the air, no question about it."
A spokesman for Westminster City Council said: "What the Top Gear team did on the day was not what had been agreed during the planning process.
"At no time had the BBC producers made Westminster City Council aware that the car was going to be doing anything but drive down Whitehall.
"There was no discussion about wheel spins and a doughnut and permission would not have been given to do so."
The spokesman also said the council had spoken to the Top Gear producers on Monday "to express our disappointment".
The council said it welcomed Mr Evans's statement regarding his belief that the footage should not be shown.
"We are very sorry for any upset that has been caused and will be strengthening our procedures to make sure that film and TV production companies will not deviate from pre-agreed plans in the future," the spokesman added.
On Monday morning, Evans apologised on air during his BBC Radio 2 breakfast show.
Referring to photos of the stunt printed in newspapers, Evans said he wanted to "apologise unreservedly for what these images seem to portray".
"They look entirely disrespectful, which of course was not and would never be the intention of the Top Gear team, or Matt [LeBlanc].
"The images on the front pages of the papers today - it doesn't matter what actually happened - what is important is what these images look like," he said.
"It does not look good at all. There have been some completely incendiary comments written alongside these pictures and I completely understand all this furore, but the Top Gear team would never, ever, do that.
"Retrospectively it was unwise to be anywhere near the Cenotaph with this motorcar," he added.
"Doughnuts" - which have previously been performed many times on Top Gear - usually involve rotating the rear of a car around the front, a technique caused by making the rear wheels of a car spin more quickly than the front set.
They often leave circular skid marks on the road and sometimes cause smoke to emit from tyres due to friction.
These images demonstrate how the use of perspective in a photograph can lead to the distance between objects being expanded or compressed, so they appear either further apart or closer together than they actually are.
Evans's comments came after a former British military commander had criticised the stunt during an interview with BBC Radio 5 live.
Col Richard Kemp told Stephen Nolan the war memorial should be shown "respect".
Col Kemp likened the Cenotaph to a "cemetery" and said he did not want to see any clips featuring the memorial in the final edit.
Sir Roger Moore has also criticised the Top Gear team for filming near the Cenotaph.
The former James Bond actor tweeted: "I was brought up to respect those who laid down their lives for this country. Shame on Top Gear and the BBC."
Perry McCarthy, who was the non-speaking racing driver known as The Stig in the first two series of Top Gear fronted by Jeremy Clarkson, said Chris Evans's view that the footage shouldn't be shown was "disappointing".
He told BBC Radio 5 live: "It's a question of perspective. It's a stunt.
"It brings the centre of London, a beautiful part of London and the Cenotaph, to a worldwide audience. It was a respectful distance away from it.
"The one shared opinion we all have is what the Cenotaph is there for, who we are remembering.
"There is no problem there of course. But come on, lighten up everybody."
LeBlanc and rally driver Ken Block also appeared to gatecrash a wedding at St Paul's Cathedral on Saturday, although it later transpired that this was staged by actors for the show.
The new series of the BBC Two programme is due to start in May.