My sister Rosemary died of cancer in March, aged 61. As her next-of-kin, it fell to me to organise her funeral. The undertaker's office, I soon discovered, is no place for the bereaved. You can't afford to be dazed or vulnerable, otherwise you will weakly agree to all the standard things, which was not what my sister wanted.

I fought against a wooden coffin and a hearse – securing, after some negotiation, a final journey in a cardboard coffin in the back of a Volvo estate. (Don't worry. It was black.) Then the undertaker asked what religion my sister was. "Atheist," I replied. That, of course, was a nonsense. Atheism is – doh! – not a religion. In that case, he asked, who was going to conduct the funeral? If the Volvo was the unconventional substitute for the hearse, who was the unconventional substitute for the vicar?

Illustration by Otto Dettmer

Happily – I insist on that word – it was me. Told before Christmas that she had months to live, my sister had the inclination and the courage to prescribe the kind of service she wanted and ask me to conduct it. What she wanted, in a word, was a godless funeral. How easy was that to achieve?

In many ways, the planning of a godless funeral was a liberation. For our mother's cremation we had, via that secular miracle the internet, procured the services of a rabbi. (Oh yes, my sister's non-religion was, in fact, "Jewish atheist".) He recited the prayers with commendable gusto. But he was much like the vicar so familiar from Church of England funerals – he didn't know the deceased; he couldn't eulogise her, except to say he'd heard nice things about her from her family. How many times have you shifted in your pew with embarrassment, as a vicar tries to celebrate a member of his flock who, it's soon apparent, is a bit of a mystery sheep? I knew my elder sister for all but the first four years of her life. In celebrating her, I had infinitely more knowledge and authority than a religious intermediary only doing his or her job.

So. I would talk about her, as would two old friends she nominated.

Then what? How, in the name of godless, would we fill our allotted span? Rosemary wanted a silence, to allow everyone to think their own thoughts. To that – without telling her, for fear of embarrassment – I added a coda, derived from those football matches in which the crowd observes a minute's silence for a dead former player or manager: that silence is followed by rousing applause, which somehow conveys: "Thank you for everything. But now we have to get on with the game."

So that is what we did at my sister's funeral: I announced there would be a silence, at the end of which everyone should applaud, long and loudly, to give thanks for Rosemary's life. It worked wonderfully, though I say it myself. Others might call it gimmicky and new-fangled. At a religious funeral you draw on rituals and prayers with the gravitas only centuries of usage can bring. You take from The Book of Common Prayer, the liturgy, the Qur'an, the Torah; but there we were, at my sister's funeral, paying homage to Match of the Day.

Eulogies and silence, Rosemary felt, should be punctuated by music. ("Do you think I'm being too controlling?" she asked, as she sat on her sofa, scribbling notes about her own funeral. "Of course not," I said, making a mental note to tell the congregation of her question. For that is another benefit of a godless funeral: humour can be encouraged.)

Without hesitation, she specified the opening song. Nothing, she said, more evoked her early childhood than We Plough the Fields and Scatter. Brilliant. Now I could stand up and say, as I duly did: "By the power invested in me by my sister and Richard Dawkins, please stand and sing We Plough the Fields and Scatter." To return to Match of the Day, it certainly felt like an early away goal for God. More such goals were to follow. She wanted Milton's On His Blindness, about a man who, in losing his sight, finds that his soul is "more bent / To serve therewith my Maker". I could go on. And I will.

She craved the Lacrimosa from Mozart's Requiem Mass: "Huic ergo parce, Deus, pie Jesu Domine, dona eis requiem." Yes indeed. Amen to that.

She may not have wanted Him at her funeral, but she needed Him. My sister, born in England in 1949, a singer of hymns in her primary school, grew up with Him. She knew that He elevates. God is the man for the big occasion. So, this is what I hope will happen before my own funeral: there'll be a great state occasion that is godless, to give hope and a kind of validation to all of us who want to live and die as non-believers.

Imagine it: a state funeral or a service of remembrance for those killed in war, in a crematorium, built by Zaha Hadid, as awesome as St Paul's Cathedral. Now imagine this: a royal wedding in Westminster register office, with a registrar standing in the archbishop of Canterbury's God-fearing shoes, as the unbelieving bride enters to the sound of an ancient and venerated secular love song, of the order of the Beatles' Here, There and Everywhere.

Unthinkable, isn't it? Treasonable, probably. Socially embarrassing, certainly. We are not a religiously observant nation – except when it really counts.