David and Victoria Beckham did not request a fly-past by World War II aircraft during a pre-World Cup party at their home, a spokesman insists.
A host of celebrities are expected to attend the Beckhams' party
Reports that such a fly-past was to take place had led to claims of insensitivity, given that the competition is taking place in Germany.
The reports were based on comments by a Royal Air Force spokesman.
But a spokesman for the England captain and his wife told the BBC News website: "It was never going to happen."
He added that a small aerobatic show by a private display team, The Blades, using more modern American aircraft, would be taking place.
The RAF had said that a fly-past by a Lancaster, Spitfire and Hurricane would be a fitting tribute to the England team.
The three planes were already scheduled to appear at an air show organised by the Imperial War Museum at Duxford in Cambridgeshire before returning to their base at RAF Coningsby in Lincolnshire.
As the aircraft would be flying back at about the same time as the Beckhams' party, the RAF had offered to make a minor detour to open the event.
But a Ministry of Defence spokesman said the fly-past had been cancelled at the request of the Beckhams.
The Beckhams' spokesman said the offer of having the three WWII planes had been suggested as part of the package on offer by the organisers of the aerobatic display.
"We declined, all we wanted was the display by the American planes. Having World War II planes was never going to happen, but there was confusion and some people thought that we were.
"The idea had been talked over by the organisers with the RAF as a possibility, but we had already decided not to go ahead on Friday.
"David has been a keen supporter of the FA's guidance for no references to the Second World War, so anyone trying to make out that we pulled out due to pressure is wrong.
"The aerobatic display was just to add a bit of excitement to the evening for the guests - if people use this... to criticise David and Victoria, that's completely wrong," said their spokesman.
"They are doing a lot to raise money for children's charities and those attending will be donating too."
The England football captain and his wife have organised the party as a send-off for his team-mates before the World Cup in Germany this summer.
Some 500 celebrities are expected to attend the Full Length and Fabulous Ball, at which pop star Robbie Williams is due to perform.
An unnamed person has successfully bid £103,000 for two tickets to attend the event, with the proceeds going to children's charity the NSPCC.
The Blades are led by former Red Arrows' pilot Andy Offer and feature other former Red Arrows fliers.