He added: "Then I asked my father. He was thrilled at the idea.
As part of a celebration of the show's 50th anniversary Radio 2 broadcast a revival of some the earliest Goon Show scripts.
The parts of Spike Milligan and Peter Sellers are played by Jon Glover and Jeffrey Holland, alongside Andrew Secombe and announcer Christopher Timothy.
Andrew Secombe, 48, said that at first he was against the idea of taking on his father's classic Neddie Seagoon role: "I told my wife about the ridiculous idea and much to my surprise she said it sounded like fun.
He added: "Then I asked my father. He was thrilled at the idea.
"Think of it as taking over the family business."
Producer Dirk Maggs has worked for 10 years to resurrect the scripts, which come from Goon shows never recorded by the BBC.
Maggs found the show's old big band music arrangements in the BBC library and arranged for Lance Ellington - son of the original show's Ray Ellington - to sing with the band.
Crazy People
The anniversary show was recorded in March at London's Playhouse Theatre, where the Goons once recorded.
The show will be part of nearly three hours of Goon celebrations on Radio 2, 50 years and one day after the BBC first broadcast the Goons under the original title, Crazy People.
The series soon gained a cult following, delighting audiences and baffling BBC bosses - who reportedly tried to suppress it 30 times - but it lasted until 1960 and a total of 243 programmes.
Spike Milligan, who also wrote the scripts, is now the only surviving member of the Goons.
'Tribute'
Peter Sellers died of a heart attack in July 1980, early member Michael Bentine in November 1996 and Sir Harry Secombe in April of this year.
"In the light of subsequent events, I am doubly pleased that I took part in what I now like to think of as a tribute to my late father," said Andrew Secombe.
"Unfortunately, he never heard the programme, but I am sure what his response would have been.
"If they have radios up there, heaven will resound to his high-pitched chuckle and a volley of fruity raspberries."