Harold Jellicoe Percival, who was known as Coe, served as ground crew on the famous Dambusters raids carried out in May 1943 by 617 Squadron.
Mr Percival, who died last month aged 99, never married or had children.
The funeral home organising the service put an advert in a newspaper appealing for people to attend.
The Reverend Alan Clark, who conducted the service, said: "We marvel at the power of the printed word, whether on paper or screen."
Mr Percival's nephew, Andrew Colyer-Worrsall, said the attendance was "just remarkable".
"He was a quiet man, he was an ordinary man who did his duty and served in the war and to see so many people turn up, it's just overwhelming," he said.
"I can only say thank you so much to everybody.
"We thought there would just be two or three of us, so to see this many hundreds of people turn up is stunning."
Mr Percival, who lived in Penge, south London, before joining Bomber Command, died in Alistre Lodge Nursing Home in Lytham St Annes in Lancashire.
Nursing home manager Lorraine Holt told BBC News she had been inundated with responses from people after the advert was reposted on social media sites.
"Late last night, we had a call from a soldier on leave from Afghanistan who said he wanted to attend.
"Then an 80-year-old lady from London who served in the RAF called us to say she was attending.
"The response has been absolutely incredible."
The RAF Association Leyland branch, said they had also helped to ensure Mr Percival's funeral on Monday was well attended.
By Steve BeckerBBC Radio Lancashire reporter
Harold Percival was, by all accounts, something of a loner, with no close family or friends.
Yet hundreds of people attended Lytham Crematorium to pay their respects, as a testimony to the power of remembrance and social networking.
With the service taking place on Armistice Day, it became a particularly poignant event, drawing armed forces personnel,  charities and many members of the public.
In fact, before the Last Post was played, a spontaneous round of applause broke out as his coffin was taken from the hearse.
We'll never know the answer to the question posed by many people at the service: what would this quiet man have made of his send off?
But most suspected he'd have been secretly pleased and proud.
The association's standard bearer Stuart Dagger said: "We are saying goodbye to a hero."
The Dambusters March played as Mr Percival's coffin was carried into Lytham Park Crematorium at 11:00 GMT on Armistice Day.
A two-minute silence was observed around the coffin to mark the anniversary of the World War One armistice before it was carried into the crematorium.
About 100 people were inside with another 400 standing silently outside in the rain.
Relatives of Mr Percival thanked those who attended and who spread the word saying "We are overwhelmed. This shows how great the British public are."
Mr Percival's nephew, David Worsell, who could not attend the funeral, said: "He was a private man.
"He worked in Australia for a number of years as a decorator and would visit England for holidays.
"He travelled around England with only his backpack.
"He didn't have a postal address - he just used to get everything sent to my mother's address and would go through it when they met up."
Frank Richard Carew-Percival, who contacted the BBC from Australia, said he was Mr Percival's nephew and was disappointed that he wouldn't be able to attend the service.
"He lived with us on and off in Australia and New Zealand. He loved cricket and taught my son how to spin bowl."
He said his uncle was a shy man who led a "nomadic type " lifestyle.
"I managed to trace him six months ago and sent him photos of when he lived with us.
"We always had a Coe's room wherever we lived as he could turn up at any time."
Mr Percival's family told the BBC a nephew, great-nephew and great-niece would be at his funeral.
Hundreds of people from across the UK have attended the funeral in Lancashire of a World War Two veteran they never knew.