Sitting with Pete Greig on the fifth floor of his publisher Hodder Faith's offices inside Carmelite House at Victoria Embankment in London, you could be forgiven for being distracted by the view.

For appropriately enough given that Greig is the founder of the massively successful 24-7 prayer movement, St Paul's Cathedral looms large out the window, just along the river, its imposing dome still dominant in the autumnal City skyline.

But with a magnetic presence, Greig has a way of transfixing you as he talks passionately over coffee about the revival of prayer in this land and beyond.

Like his new book Dirty Glory, Greig is gripping, gritty and optimistic.

We start by discussing how the 24-7 prayer movement went beyond a passing fashion to sustain itself as one of the most exciting evangelical movements on earth.

"If you'd said to me, here's a good idea I'd have told you it was a bad idea," Greig says. "But it just happened. We started one prayer room because we figured that that is the heart not just of the Christian faith but actually of humanity, and amazing things began to happen as we set time apart for prayer, and it began to spread, and we're now...working with everyone from the Salvation Army through to the Catholic Church...So it's a truly viral movement. Obviously we have had to try and get organised without becoming a sort of organisation in the classic sense of that word. But I think it would be true to say we are still surfing waves rather than making them, which is more fun and easier."

After clearing his diary following a spiritual drought and a deep hunger for a true connection to Jesus in the summer of 1999, this theology graduate and church planter launched the 24-7 prayer community which now operates out of over half the nations of the world. Dirty Glory, which has been praised by Justin Welby and Bear Grylls among others, is a collection of personal stories from the past 15 years interwoven with verses from the Bible and insights from saints and other Christian thinkers.

There are many elements that make the book stand apart from your standard 'happy clappy' evangelical book. It honestly deals with pain, not least Greig's wife Sammy's struggles with life-threatening illness, which made the couple question some of their decisions to follow Jesus' call wherever it took them around the world.

As Greig writes, "...if this is a glory story it is a peculiar kind of glory, mostly touching down in broken places and messed up people who rarely feel as spiritual as the story makes them sound."

Something else that makes Dirty Glory stand out is Greig's commitment to social justice, on which an entire section of this lengthy book is devoted.

The author pauses and is thoughtful when asked what social justice means for Christians in this world today. "Dostoevsky says that without God there is no morality. If we are all just highly evolved animals then it's survival of the fittest. And the weak – in Aleppo [in Syria], or in a local cancer ward – on Darwinian theory they should be wiped out of the gene pool: I consider that an outrageous world view," he says.

"To believe in justice is to believe in the morality of God, to believe that the weak and the marginalised and the oppressed, that their suffering matters. We have a coherent rationale for that passion, and that is why the church is the biggest provider of Aids care on earth. That is why the church in this country runs more schools and youth clubs and toddler clubs and networks of debt counsellors and feeds more families than any other voluntary agency. This is what Christians have always done. It's a deeply biblical theme. When Jesus came and said 'this is my mission statement' he chose Isaiah 61 which says 'The spirit of the Lord is on me, bring good news to the poor.' So you cannot be a Christian and be unconcerned about the refugee crisis. You cannot be a Christian and be more interested in Angelina Jolie and Brad Pitt's divorce than what's happening in Aleppo. To be a Christian is to be concerned about the brokenness in our world and to do something about it."

Greig's journey with 24-7, as outlined in his earlier book Red Moon Rising, began with a vision when he was travelling in Cape St Vincent in Portugal, where he saw an army of thousands of young people rising up. He would return to the same spot and find himself there, perhaps providentially, on September 11, 2001, when his mission would be recharged.

In Dirty Glory, Greig writes that his "thinking" about the movement and about prayer has moved on since Red Moon Rising. How so?

"We've been praying non-stop for 17 years. We've been in a fairly constant state of bewilderment for much of that time, and we've also gone through some very painful things, for me personally – I've been very open about my own wife's chronic illness – and inevitable that shapes your theology and your outlook on life," he says.

"I would say that we've broadened our understanding of prayer, from seeing it as some switch that we have to flick to make stuff happen, to understanding a more contemplative dimension of becoming the prayer, not just prayer as a verb but as a noun. We are probably more comfortable with paradox than we used to be, but that might just be getting older. And I think as well we've had to learn just to get a little more organised."

Greig found himself caught by surprise over the movement's success, and he is surprisingly honest about how he and his team had to improvise. "I mean, I never wanted or knew how to lead an international organisation. It was never a desire or a drive in my life. Finding myself doing it, we've just had to work out as we go along, how do we do that, how do you have charitable status in that many countries, how does it fit together, how do we stay true to our values, how do we make sure that our structure is shaped by our vision but our vision is driven by our values? Institutions are all about structure. That's clearly not the way we want to go. Then the more progressive organisations tend to say it's all about the vision, but the problem with vision is it comes and goes and the world moves on, so what we're really interested in is how do you build something that is rooted in shared values, and out of that we can work out what we live and die for, what we sense is important to do this year or next year, and then we say how do we structure around the vision.

"So for us that's been a very important conversation, and the fruit of it is that we're not nearly as effective or as an impressive as we would like to be, but we haven't had one major relational fall out in 17 years: we are truly still friends on a journey together, and for me that's worth a bit of inefficiency, some slightly lower standards. If you worship efficiency, then you have to make some sacrifices that you might not want to."

In the book, Greig talks about the need to turn the tide "back" to Jesus in our time. Asked why he uses that formula, Greig strikes a characteristically optimistic note.

"The reason I say we need to turn the tide back to Jesus is that Europe and certainly the British Isles were founded, forged by the gospel of Jesus Christ," he says. "It is actually impossible to understand why we exist or what our identity is without understanding our Christian heritage...Whether it is rock bands recording hit records at Abbey Road studios, or me ordering a pint of Abbott ale, or the fact that Big Ben broadcasts a chime that is actually a prayer every single hour to the nation, or whether it's that every single place in Ireland with the suffix 'Kil' was once a hermits' prayer cell – this is in our history and our psychology. Europe will not rediscover who we are and where we're going until we dare to be reconnected with our past and at the psychological and geographical heart of every single capital city in Europe stands a house of prayer. That is probably the key not just to where we've come from to where we're going."

Just as he was in 1999, Greig says that in his experience, "people are clearly hungry for spiritual reality." He goes on: "We find that even people who don't want to be preached at still want to be prayed for. All the surveys tell us that most people pray, whether or not they go to church. So we're in an interesting post-Christian era in which people's preferred spirituality is actually still Christian. And people's preferred humanity is still spiritual. Then within the church, there is clearly an uprising of prayer. The Archbishop of Canterbury's number one aim is the renewal of prayer and religious life in the UK. He says – and I've heard him say it often – that without a renewal of prayer there will be no renewal in the church and without a renewal in the church there's no hope for our nation.

"And we are seeing empirical evidence that people are responding to that message not least with the fact that we packed out four cathedrals and one very large church last Pentecost Sunday and there were so many at Winchester Cathedral that there were hundreds outside watching on screens, and this was not for show – it was to pray. We tracked almost 3,000 prayer initiatives in the build-up to Pentecost last year, from tiny little rural churches praying all night that would never have dreamed of doing it a few years ago, through to big prayer meetings. The Redeemed Church of God here in London has 40,000 people praying all night regularly. There's a different story out there that the press is not reflecting...There is a different story out there of renewal, because human beings are spiritual. And the vast majority of people still believe. And what we have to do is articulate that in a way that is as colourful and compelling and relevant as Jesus Christ."

Greig and Welby are clearly like-minded. What of Pope Francis, who is close to the evangelical movement? What hopes for cross-demoninational Christian unity in our time?

"I believe one of the things that God is building reconciliation between different types of Christians," Greig says. "We are sitting here now on the eve of the 500th anniversary of the Reformation, and I think one of the things that we are trying to learn is how to look at other types of Christians – not ask what's wrong with them but what's right with them. How can we be enriched by our differences rather than divided by our disagreements? And the truth is that we've got far more in common than what divides us. My background is in Free Church, but I spend a lot of my time now working particularly with Anglicans and Catholics, and I find that enormously enriching."

A crucial pillar of that unity, for Greig, is the Nicene Creed of 325 AD. "All Christians of every tradition agree with that statement of faith," he says.

Like many church leaders and, indeed, perhaps the quiet majority of lay believers, Greig is keen that Christians do not get too distracted by "secondary issues".

He says: "There are all sorts of things that people get terribly passionate about – ranging from gay marriage through to women in leadership through to the role of Israel through to the gifts of the Holy Spirit – these things are all vitally important but they are secondary to the primary issues, the essentials, as articulated in the Nicene Creed. And if the church of Jesus is to be united, we must prioritise the vocabulary given to us by that ancient agreement, and not allow secondary issues to divide us."

Above all, Greig says: "There's a desperate need for us to slow down".

Finally, asked what he would say to those who struggle with prayer, who fail to achieve that personal relationship which Greig talks about in his book, one which involves discussing the "trivial" as well as the fundamental, Greig is concise.

"My advice on prayer is keep it simple, keep it real and keep it up."