First, and most importantly, he corrects the wrong impression given by the title of his most famous book, The Selfish Gene. Many people took this to mean that he thought that human beings had no option but to act selfishly. Quite the contrary. At a personal level, Dawkins believes that whatever the evolutionary processes that have brought us where we are, we have a responsibility to act as moral agents.

He grounds this in the fact that although genes always act in such a way as to maximise their chance of replicating themselves, the organism of which they are a part may in fact act altruistically, this being the way the genes optimise their chance of surviving. He gives four examples of this, two being well-known. One is how mammals can act with great altruism on behalf of their offspring. Another is the reciprocal benefits that flowers and bees bring to each other through the process of pollination. This co-operation increases the chances of the genes of each of them surviving.

In a more speculative way, Dawkins then builds on this in suggesting that as the sex instinct is not limited to reproduction but can find a broader focus in its contribution to culture, so this capacity to think of others is no longer confined to helping kin or forms of reciprocal altruism, but can find wider expressions. From a philosophical point of view, this is important in refuting the idea that as humans we will always be driven by considerations of narrow self-interest, that morality is unnatural to our evolutionary make-up. On the contrary, Dawkins shows that it is just as built-in for mammals such as ourselves to act in the interest of others. Morality is part of our nature.

Dawkins also draws on the work of Peter Singer and Marc Hauser who presented two moral dilemmas to a wide range of people. In the first, a railway truck careering out of control down a track is about to kill five people in the way. But the onlooker has the chance of pulling a lever and diverting the truck on to a siding where there is one person standing, who will inevitably be killed. Do you pull the lever? The vast majority of people of all ages, ethnic and cultural backgrounds said yes.

In the other dilemma, there is no lever or siding, but a bridge on which sits a very fat man. If this man is pushed and falls in front of the truck, it will be stopped and save five lives. The onlooker is too light to make any difference to the truck, so jumping himself would serve no good purpose. But he is strong enough to push the fat man off. Should he do it? The vast majority of people, again from every conceivable background, said no.

Peter Singer draws some conclusions from this that I do not want to do myself, but the important point is that people's moral judgments have far more in common than used to be thought. There was a time when people loved to emphasise the alleged differences between different societies and hence the relativity of all moral judgments. But it seems we all inhabit a moral realm which we can recognise as such.

This is no surprise to monotheists who believe that all of us, whatever we believe or do not believe, have been created in the image of God and this means we have an ability not only to think, but to have some insight into what is right and what is wrong. In its most philosophical form, it is a belief in natural law, and in its most advanced legal form, a belief in universal human rights.

Dostoevsky's Ivan Karamazov said: 'If God did not exist, everything would be permitted.' Sartre agreed. Dawkins disagrees. Morality belongs to us as human beings. I agree too. I do not believe that a society without a religious basis for its morality will always collapse. But I do think that the relationship between morality and religion is more complex than either Dawkins or religious believers usually allow. Take an analogy: someone hears a great piece of music and responds to it in itself. But someone else knows that the piece is part of a symphony and can be even more appreciated when heard as part of the whole in which it has a crucial place. As human beings we can recognise and respond to particular moral insights. But a religious believer claims to understand these as part of a much larger whole in which they have a vital place: in particular, there is a fount and origin of all our moral insights which is good, perfect good, all good, our true and everlasting good. For a Christian, this is above all shown in the willingness of God to enter the flux of history, to redeem it from within.

Religious people have been at fault in the past for slagging off moralities that did not have a faith basis. Today, it is the other way round, with religion being widely criticised for stopping people acting with moral maturity. But the crisis of moral values is such that we should simply recognise and rejoice in the good wherever it is to be found, while continuing to converse about whether it has its place in a larger scheme of things.

Commenting on the view that a society without religion will collapse, Dawkins writes: 'Perhaps naively, I have inclined towards a less cynical view of human nature than Ivan Karamazov. Do we really need policing - whether by God or each other - in order to stop us from behaving in a selfish and criminal manner? I dearly want to believe that I do not need such surveillance - and nor, dear reader, do you.'

But this overlooks a number of points. First, many people who have strong moral commitments without any religious foundation were shaped by parents or grandparents for whom morality and religion were fundamentally bound up. Moreover, many of those in the forefront of progressive political change, who have abandoned religion, have been driven by a humanism that has been essentially built up by our Christian heritage as Charles Taylor has recently brought out in his magisterial study, A Secular Age. How far are we living on moral capital?

Then, although I believe there is a shard of goodness in every human person, there is a dark side to our nature that it is sentimental to ignore, one which is still wreaking such terrible havoc. As WH Auden put it: 'We have to love our crooked neighbour with our crooked heart.' This points to the need for both self-knowledge and grace. At the beginning of this new year, with the world so stricken with growing inequality, corruption, decadence and conflict, each of us, believer and unbeliever alike, need all the help we can get.

· Richard Harries (Lord Harries of Pentregarth) was Bishop of Oxford. His book, The Re-enchantment of Morality: Wisdom for a Troubled World, is published by SPCK next month