The following is an excerpt from the Archbishop of York's new book, Dear England: Finding Hope, Taking Heart and Changing the World, out this week in hardback from Hodder and Stoughton, priced £12.99.

Dear England,

I was recently buying a coffee at Caffè Nero on Paddington Station. A flat white. This was a wise decision. The coffee from Caffè Nero is nicer than the coffee from the trolley on the Virgin train. I was on my way to Cardiff. The keynote speaker at the Church in Wales symposium on evangelism. It was a big gig. I couldn't be late. The Church in Wales was relying on me.

While the barista prepared my coffee (buying coffee never used to be so complicated, but a flat white seems to me to have got the proportions of coffee to frothy milk about right), a young woman turned to me, looked me up and down, and said, 'What made you become a priest?'

Now this is an interesting question. In fact, it is my standard interview question. I've asked virtually every priest I've appointed in the last fifteen years what they would say if they bumped into an old friend on a railway platform and were asked why they were a Christian and what difference it made to their lives. Now a complete stranger was asking me my interview question. For real. And I didn't have long to answer. I had to get that train.

So I resisted the temptation to ask her in return why she was asking me. After all, it wasn't my natural aura of holiness that was giving me away. I was dressed as a priest. I said I had two answers to her question: one, a very short answer; and one, a slightly longer answer.

My first answer, the short answer, is God. I said to her that I simply believed in God. That, even though I wasn't brought up going to church, somewhere and somehow on the pathway of my life as I had sought to make sense of what it is to be human and what inhabiting this world could mean, I came to reckon that there is a God and that God is the source, the impetus and the precondition of everything.

It hadn't been a sudden, thunderbolt conversion, nor did it mean I was unfamiliar with doubt and darkness. It's just that I had tried to make sense of life, and looked for some meaning in life, and had arrived at a point where life, the universe and everything in it made no sense without God. Moreover, as a Christian, when I said the word 'God', I saw in my heart the person Jesus. Jesus was the person through whom God had a human face and a human heart.

Therefore, the God who was in every other respect unknowable and beyond, the source of everything but, by definition, outside of everything as well, had come down to earth, so that God could be known. Jesus was God speaking to us in the only language we understand: which is the language of another human life. That was the short answer!

The slightly longer answer was that I wanted to change the world. I asked her what she thought and felt when she looked at the world, and I told her what I saw was hurt and confusion. Oh, of course, there were fantastically beautiful, glorious and wonderful things as well. The world is brimming with expectancy and elation. But there is also injustice and horror, and while those persist, joy would always be tempered by caution and concern. I also told her that I had made a diagnosis. I told her I thought the problem lay in the human heart. I told her that I thought the human race needed a heart transplant. And I told her that, as I saw it, only God could do that.

Why was I a priest? Or for that matter, why am I a Christian? Why am I a follower of Jesus Christ? Why am I writing this letter that thinks it's a book? It is because I believe in God and I want to change the world. But I don't believe in God in quite the same way as I believe the sky is blue and the sun rises in the east. It is much more like I believe that love is real and that Chopin's nocturnes make me cry. Some things are achingly real, but harder to demonstrate, though dig beneath the surface and we all deal in the common currency of love.

And I want to change the world – heart by heart. I cry out for the indignities and privations of the world. I long to see change and I thirst for justice. But I begin with the heart, believing that if my heart can change, then the world can change too.

The woman then said to me – and in many respects her words were much more interesting than mine – that when she met people of faith, she found they largely broke down into two categories. For the first group, faith seemed to be their hobby. They went to church – or, for that matter, the synagogue, the mosque, the temple – but it didn't make much difference to the life they led. In most ways their lives were indistinguishable from other people's lives, except for the fact that they went to church on Sunday. The other group – and these are her precise words; they seared themselves into mymind – 'embraced their faith so tightly, it frightened everyone else away'. (Perhaps your experience has been similar.)

'Is there another way?' she asked me.

But at this point, I had to get the train. I couldn't miss it. There wasn't time for the conversation I thought we needed to have. So I just said, yes, there was another way: the way of Jesus Christ. I said that Christians believe that Jesus not only showed us what God is like, but shows us what humanity could be like. I told her to go to her local church and she would find it.

But that's what really bothers me. If she did follow my advice and go to her local church, wherever that was, what would she find? Would she find a group of people who are joyfully trying to inhabit this world after the way of Christ? Or would it be a group of Christian hobbyists? Or something worse?

So this is what this book is about. It is a letter to this young woman, for I saw in her something that I see in so much of our culture. She was genuinely seeking for some meaning in her life beyond herself and beyond the things she had already been taught and experienced. She initiated the conversation, not me. Amazingly, she saw in my clerical collar (and hopefully in my demeanour) some representation of a worldview that might just scratch the itch of her spiritual longing.

This book is what I would have said to her if I had had more time. And in a small way it is also a letter to the Church of England (and other churches are welcome to receive it too if they'd like). I want to remind us that our primary vocation is to share this story and to tell people about God and God's vision for the world.

There are lots of other things we need to do as well – not least live it out each day – but it has to begin with the story itself: the amazing, inexplicable, challenging and lovely story of what God has done in Jesus Christ to change the course of human history and to win our hearts.

And I've called it Dear England because in writing to this woman I am also, if it doesn't sound too presumptuous, trying to write to everyone. The moorings of our culture have slipped from the passage of the Christian way, and other, sometimes malign and confused, currents now sweep us this way and that and leave us not knowing who we are, still less where we are going.

This book can't solve all that, but in reading it (and reading it won't take long; it is not a hefty tome) you might see something of God and something of God's purposes for the world. The very first Christians weren't called Christians, they were called followers of the way.

I like that sobriquet. It indicates a pathway to follow rather than a list of things to believe in. In fact, Jesus himself said, 'I am the way.' He is a companion, not a map. Let us see what life looks like if we walk with him.