He was in fiery mood. ''Part of our problem today," he said, "is that because we have all become so accepting and charitable towards one another - and I am not disagreeing with charity at all - we have, maybe, lost the art of judging what is right from wrong, or assessing what is deviancy as opposed to normality. We are in danger of becoming a shallow society, focused on consumerism.''
Where, in the past, even people on the edge of the Church, like Thomas Hardy and George Eliot, went along with the general Christian consensus, ''when you have a society in which unbelief has become the norm and practising Christianity a minority pursuit, then you have to raise the question, what are the shared values that hold us together?''
He would wait to see whether changing morality was a trend, but ''people will not be surprised if, as a Christian leader, I am going to be warning against that and actually questioning whether it is going to lead to the collapse of the kind of civilisation as we have known it.''
Few pulled punches there. But wasn't he in the situation of political leaders, who jerked the old levers of authority and found that they no longer worked?
Dr Carey replied that he wasn't someone who looked back to a golden age before the Sixties, and he wasn't worried that authority was being questioned. ''But we have lost a sense of community and I have been warning against the loss of sense of shared values that used to bind us together ... whereas the politicians seem to think that what essentially matters is economic order and prosperity and consumerism.'' He was all for wealth creation, but ''the real fabric of society is the spiritual and moral fabric, and this is the kind of currency that makes civilisations function.''
For a long time Britain had been living off the legacy of the past which had been strongly Judaeo-Christian and a shared sense of values, but that legacy was now being questioned. The Church had a prophetic role in the country to say, ''you can only have good citizenship if it is based upon common values which we all acknowledge and if no rigid distinction is made between 'personal' morality and public morality.''
He was, then, one of those who thought that people's individual private lives affected their public role? The Archbishop was strongly critical of press intrusion and harassment but added, pretty firmly: ''I regard morality as indivisible and what a person gets up to in public life acutely affects his personal life and vice versa.''
The Archbishop accepted my point that morality seemed to change - once it was thought immoral to be homosexual, now it is thought immoral to be homophobic - but returned to what he called the common ground of the Ten Commandments and the teaching of Christ. I reminded him that he had used the phrase, ''the privatisation of morality'' to criticise modern Britain.
Was he advocating the renationalisation of morality? ''Yes, yes. Or we can say public ownership of morality. We ought not to be ashamed of goodness, righteousness, honesty, duty ... We've lost a language of blame and sin. The word 'sin' is now a word dying, leaving our vocabulary. Was it Oscar Wilde who said the distinction between man and animals is that man knows how to blush? I wonder if we've lost a sense of shame. And I think that's something we need to work on.''
That, I suggested, made him sound like a communitarian (those American and British social thinkers who have attracted growing support both on the right and from leaders such as Bill Clinton and Tony Blair.) He agreed: ''Communitarianism is a form that unites all those interested in values - Christian and non-Christian - and therefore I think that's a very helpful debate going on. Sometimes I wonder mischievously if these words are really just saying the same thing as what we meant by community and community values and so on; but we are talking about how we can create again a society based upon common values that we all own; and all share; and what they are showing actually is the importance of all these elements - religion included - as part of the solidarity which binds people together.''
This was all very well, but if political leaders were unable to get their messages over, how would he succeed? In the age of mass media, the internet and so on, he was off to speak on morality to the House of Lords!
I got a remarkably frank response: ''When I am at my most pessimistic moment, I sometimes wonder how anybody can possibly put back into society something which is central to its existence, and something which seems to be lost ... I seriously doubt whether we can actually do any more than blow trumpets from castle tops and warn. But the other side of me says that actually there is such goodwill in society...
"In the Sixties I experienced in my parish ministry some hostility. There was a lot of triumphalism around, which seemed to say, 'well we don't need this thing called faith'.'' That was changing; there was more openness. Later he returned to the problem and said: ''When I am back to my most pessimistic moment, I could say you throw up your hands and walk away from it. You don't ... I am like the salmon going upstream. You have got to fight against this.''
So what, in practical terms, were his weapons for the fight? The Archbishop replied that he wanted to ignite a national debate. ''It will require a partnership between the school, parents, government, the media'' to return Britain to the ''good society, founded upon the principles which I regard as essentially Christian.
''It has to start with Sunday schools, with churches, in family life ... When I talk to teachers, I notice their concern that they don't feel they have the support of families any longer. They are often caught up in the task of actually doing jobs that the parents should be doing, which is bringing children up to be moral ... parents are also perhaps to blame in not doing their job of parenting.''
There was a role too for the wider community, though Dr Carey made it clear he thought that remoralisation had to be led by religious people: ''Any religious person is going to say that when you work from the end of life, that is the thing that sets out the value ... The challenge facing atheists is, have they got an ideological basis for ethical standards?
"I would want to challenge them on that particular point. What is the basis? That is not to say they can't be good. Indeed they are, many of them, very good, very moral people, But I want to question whether there is a logic there, whereas religious people have obviously got a logic.''
Since we were now talking about the moral condition of non-Christians, I asked him what he thought about the pre-millennium mood, the New Ageism and the rest of it. He acknowledged that ''the mainstream churches are being challenged by New Age religions and Eastern religions, and maybe what we have got to face up to is that we have lived off the outside of our faith for too long ... Maybe what we have got to learn is to return to the depths of faith.''
He wants to use the anniversary next year of the coming of St Augustine to Canterbury in 597 and the death of St Columba on Iona in the same year to begin some pre-millennium crusading of his own. ''You have got the great movement of the Celtic mission in the north and then in the south, the Latin Roman mission. I think we may well find we will be able to tap some of this spirituality ... I think the Church must grab the opportunity of the Millennium, and indeed I and my colleagues in recent months have been reminding the Government that the year 2000 would have no significance if it wasn't related to the birth of Jesus Christ, and therefore is essentially a Christian anniversary, a Christian party to which everyone is welcome.''
The Archbishop has recently announced that he is to visit the Pope in December. The Vatican is very keen on making the year 2000 a focus for Christian unity, but I suggested to Dr Carey that, while personal relations were good, the distance between Canterbury and Rome remained large.
''Yes ... personal relationships are very warm, very wholesome indeed; and I have worked, and other people have worked hard, at securing that. And I have got the highest regard for the Pope as an individual, as a fine Christian leader.'' There had been some important theological agreements. But ''where we are far apart will be on the infallibility of the Pope; some of the Marian dogmas, celibacy of priesthood, for example; and the ordination of women more latterly ... It's going to be a long time before we can actually talk about the full visible unity.''