After 15 years as a professional writer, I have, finally, been asked to perform at The Times Cheltenham Literature Festival. For the first time, a book on which I have spent months working has not disappeared instantly without trace. Indeed, tens of thousands of copies of it - fat, juicy hardbacks with a great cover and colour plates and a dangly red page marker and everything - are piled high in every Waterstone's in the land. Furthermore, it has just completed a run as Radio 4's Book of the Week, read by John Sessions - the Holy Grail of book promotion. I am made.

Or, rather, my father is made. Made, but dead. For it is he who wrote the words in the book. All I did, with my sister, was to choose them in preference to some others of his, put them in order, come up with a title, dig out some photos and suggest the little red dangly thing.

We didn't even have to go looking for a publisher. They came to us: Canongate, the hippest publishers in the country. Publishers who have, twice, read novels of mine, tittered politely and suggested by return of post that I might want to think hard before giving up the day job. They wanted a big piece of Alan Coren, though, and they were prepared to pay for it. With actual money. Like he was J.K.Rowling or something.

They just needed someone to edit it. If my sister or I ever got any job “just because you're Alan Coren's children”, this is certainly the one. For I must confess that there was no elaborate interview process. No advert was put in The Guardian with assertions that applications from certain social segments would be looked on especially favourably.

It's a sobering thing for a columnist and broadcaster, who occasionally kicks back and allows himself to reflect that he has done pretty nicely for himself, to be reminded that, as far as most people are concerned, he is but a small offshoot of one of the most loved writers and broadcasters of a generation - a man whose words are still far funnier, 40 years after they were first written, than any of the ones I am writing now (although, to be fair, I did not set out to make this one of my most hilarious paragraphs).

We called the book Chocolate and Cuckoo Clocks in honour of the first line of his to appear in The Penguin Book of Quotations (my father loved getting into reference books): “Since both Switzerland's national products, snow and chocolate, melt, the cuckoo clock was invented solely to give tourists something to remember it by.”

As a cultural aperçu, it was no more sensitive to the insecurities of small and irrelevant countries than his observation, on an episode of Call my Bluff, that “the windmill was invented for the sole purpose of filling up the blank bits in the back of 16th-century Flemish paintings”, but it was perfect for us as a title.

You see, my father used to bang his stuff out (literally, “Bang! Bang! Bang!” - my childhood bedroom shook with the thunder of his giant old Olivetti up in the study) only to give people a bit of a laugh the following morning, or, in the old Punch days, in the hope that it might stick around for a week on a coffee table somewhere, or a little longer in a dentist's waiting room. At best, if they made it into one of his anthologies, his pieces might last just about long enough for the leaves to change colour in Basing Hill Park or for Queens Park Rangers (whose fans always peopled the bars of his mythical Cricklewood pubs, along with the talking animals, unemployed trapeze artists,14th-century plumbers and German war criminals) to drop another division. Then, like snow and chocolate, they melted away.

This book, I hope, will be the cuckoo clock. The something to remember him by. The thing that will stay in people's houses, possibly high on the wall, and may even be passed on to their children. The thing that will stay in print, perhaps, and still be found in bookshops years from now, where the amphibious future humanoids who have survived whatever bio-ecological meltdown lies in store will pull it down and chortle again at Mao, He's Making Eyes at Me, without having any idea who this Mao fellow was.

They will mouth “wossname” and “narmean” to each other, and wonder what on earth they can have meant. Perhaps they will read his great parodies - The Small Gatsby, The Hell at Pooh Corner and The Gollies Karamazov - even though people have long since stopped reading whole books, and nobody knows who Dostoevsky or Scott Fitzgerald were.

My father claimed 20 years ago to have written six million words, the equivalent of ten copies of War and Peace. In my laziness, I read for this book only the articles contained in his 26 published collections - a mere 5,000 pages, or twice the length of Proust. And I chose the ones that, in the mood of that morning, afternoon or night, made me laugh the most. You'll probably say that I chose all the wrong ones - Where are The Chronicles of Magoon? What of The Peanut Papers? But you have to remember that my sister and I came on board as readers only relatively late - as much as 25 years after his earliest fans. But it doesn't matter, because they're all brilliant.

I didn't read as much of his stuff as I should have done when he was alive, and so it felt a very good, circular, completing sort of a thing to be reading it all now. And it really wasn't more than two or three times an hour that I found myself thinking: “God, that's funny, that line is bloody genius, I'll phone him now and tell - oh.”

But maybe if I'd read it when he was alive and phoned to tell him how good it was, he'd only have said: “Can't speak now, Jig, Countdown's about to come on.”

I hope he'd have been happy with the pieces we've chosen. After all, we've got Let us now Phone Famous Men, and £10.66 and all That, and Go Easy, Mr Beethoven, That Was Your Fifth! And we've got the piece (unrelated to the title quote) in which he finds that his cuckoo clock isn't working because the cuckoo has disappeared, and is baffled: “I searched the kitchen floor. Nothing. Had a clockwork cat got in?”

We have the famous tale of 007 at 70, which begins: “Bond tensed in the darkness and reached for his teeth.” We've got “the fags are going out all over Europe, not to be lit again in our lifetime”. And we've got the bit where my dad declares: “I have nothing against poetry. Were it not for poetry, Postman Pat would have had a black and white dog.”

And we asked some very serious people to write introductions for us to each decade of his writing - Melvyn Bragg, Clive James, Victoria Wood, Stephen Fry and A.A.Gill - and they all said yes.

And the publishers put in the red dangly thing, and used ever such expensive paper. And now everybody seems to be buying it. And so people all over England are going to be sitting around this Christmas with their feet up and a drink in their hand, chortling along with him, even though he's been dead for more than a year, lying in his six feet of Cricklewood soil, in his best suit, with a handkerchief folded in his top pocket like always.

And the great thing is that after all these years of people saying that Victoria and I only ever got published because of him, now he's getting published because of us.

So, at last, we've repaid the favour.

— Chocolate and Cuckoo Clocks: The Essential Alan Coren, is published by Canongate at £20. It is available from Times BooksFirst for £18, free p&p, 0870 1608080, timesonline.co.uk/booksfirst

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