I said yes.
"We are hoping for 13," said the man, 13 being the number of weeks for which a successful series is scheduled. This was money to be reckoned with: 12 guineas per recording it was, plus extra for any repeat and a bit more if Bush House took it to broadcast to the world.
First came the pilot: a session which would be carefully edited and played to the controller of the network. What the big man said went. He said "go".
We recorded the half-hour series and it was broadcast to modest acclaim. Just a Minute was born. "What do you think?" we asked each other when it was over, and some of us thought it might go on.
The dramatis personae settled down to three out of four, made up of Kenneth Williams, Derek Nimmo, Peter Jones and me. A woman was added partly so that listeners could identify a female voice, mostly so that Kenneth could say, "I don't think we should have women on this show", a phrase which achieved joyous reaction every time Aimi Macdonald, Sheila Hancock, June Whitfield or whoever challenged him.
Kenneth Williams had his own claque of supporters. They occupied the front of the queue that formed outside the studio for hours before the doors opened, sat in the second row and applauded every remark, every comic gesture. For Kenny the studio audience of a few hundred was infinitely more important than the millions of listeners.
Nicholas Parsons was our chairman. He had starred in the Arthur Haynes Show. I had been at school with him, employed him in cabaret when I owned a night club in the Fifties. Nicholas is one of the great "straight" men in television and was endearingly pompous sitting in governance of people who may be even brighter than he.
Just a Minute involved precisely that. Having to speak for one minute on "flooding", a panellist would begin "The Upper Volta has the lowest per annum rainfall in central Africa".
Another panellist would then buzz and say, "That is not true". Nicholas decided that calculating African rainfall was difficult; the question was best put to the audience. "All those who think Peter is right cheer - those against, boo for Derek and do it now." The audience had been unearthed by the BBC Ticket Unit, or perhaps they had come in to escape the rain. What they shouted was half-way between cheer and boo, and was so indecisive that the chairman had to decide.
We owe a great deal to our producers. They would record anything up to 10 minutes over the required time so that the worst of the irrelevant bickering could be excised. David Hatch was our first director. The story goes that Hatch, a brilliant recruit from Oxford and himself a writer and performer of humorous programmes was told after the first series of Just a Minute that it would not continue.
OK, said Hatch, neither will I.
The BBC needed Hatch, thought his work excellent ... so he and Just a Minute stayed, Hatch rising to the top of radio management before becoming head of the Consumers' Association.
Our next director was equally brilliant and the one after that was called back from retirement to control us. Then we had Jane, Sarah and Ann. Either they were excellent or else the programme has become so brilliant that anyone can do it.
When Kenneth Williams died, the BBC thought it wrong to designate a successor. Instead they introduced alternative comedians: Paul Merton, Jo Brand, Sandy Toksvig, Helen Lederer.
In the end, they settled on Paul Merton with occasional alternatives. Meanwhile, Peter Jones, Derek Nimmo and I live on: a bit slower now, no longer as keen to buzz for a transgression. (The result of a correct challenge means getting the subject - having to earn your corn the hard way.)
For reasons not altogether clear to me, we now record Just a Minute at studios around the country. On election day it was Glasgow. Parsons was debonair in a green blazer: when we were at school he was a year older than I; he is now officially seven years younger.
Derek Nimmo was always a man of gravitas and remains so - he has also found the secret of eternal hair or has an outstanding wig maker. He is immensely rich, but refers to his chateau as "my cottage in France", his mansion as "a pad in the country". His house in Kensington is "the flat".
The series that we are currently recording starts in July. "Do you think this will be the last?" I asked Nimmo on Thursday night.
"You've been asking me that for 31 years", he replied.