The veterans, all aged between 87 and 94, left the RNZAF Whenuapai base in Auckland for the unveiling of a long-awaited Bomber Command memorial in Green Park.
Mr Cunningham, of Wellington, said he went back to Belgium in 1996 and visited the cafe where he landed after parachuting to safety.
A woman working there returned part of the parachute, which she had kept and made a wedding dress from after Mr Cunningham was dragged to a Russian detention camp.
Twice he tried to escape. Once was with a former Eden College prefect Guy Pease, a soldier originally from England who studied in New Zealand and now lives in Australia.
Mr Cunningham said he remained close friends with Mr Pease, the pair sharing a special bond from their days at the camp.
"He was out here two or three years ago and we had a meal together and I said, 'you know, old habits die hard'. He said, 'what do you mean?' I said, 'well if I drop a piece of food on the ground I don't put it in the rubbish bin, I pick it up and I blow on it and I eat it'." Mr Cunningham said.
"You know what he said? 'I don't bother blowing on it'."
Stories of mateship formed during World War II will be shared by the veterans flying to London.
About 6000 New Zealanders who flew in bombing raids over Europe during the war.
More than 90 veterans applied for the Government-funded trip to London but 40 withdrew after considering the difficulty of the journey.
The approved 33 will have their international travel, accommodation and other costs including care and support teams and medical assistance paid for during the two-week trip.