The ceremony marked the 60th anniversary of Bomber Command, which lost 55,000 members of its aircrew in World War II.
The Queen Mother, as patron of the Bomber Command Association, had been due to attend the service at St Paul's Cathedral.
A Lancaster bomber completed a fly-past at the end of the service.
Flying a bomber was one of the most risky occupations during the war - it had the highest loss rate of any major branch of the British armed forces.
In fact, Bomber Command lost almost half of its serving members.
About 1,800 veterans and their families attended the hour-long service.
Twenty-four men from the Queen's Colour Squadron of the RAF regiment lined the main entrance as the Prince passed by.
Peter Lloyd, now 78, was a wireless operator from Wrexham, North Wales, who flew on 25 missions between 1944 and 1945.
He said: "It was a very moving experience. I'm sorry the Queen Mother could not be here."
Past losses
Some of the veterans were wearing medals - although there is still no official campaign medal commemorating Bomber Command.
Tom Thackeray from Guildford in Surrey, was one wearing the Distinguished Flying Medal he was awarded as a flight engineer in Bomber Command.
The 80-year-old said: "It is very important to our people because we all lost so many friends and there was such a tremendous spirit during the war.
"You cannot forget it."