Alternatively a humanistic approach despite Christianity.
That would only work if it was not for the history of Humanism within Christianity and the works of Justin the Martyr who expressed the value of classical ethical ideas and culture, this was confirmed and formed part of the Christian Theology from the 2nd Century is is also the basis for modern Secular Humanism.
Personally I would say that our morality has most certainly improved, we have a much better human rights record now than at any previous point in our history. We are eroding long standing prejudices and treating more people ethically than at any other point in our history. We would probably advance even quicker if we stopped paying attention to organisations still willing to discriminate due to gender and sexual preference.
I agree we are on a legal level (in Western Europe) in regard to certain defined examples, Human legal rights and so on, however I would be a little more pushed to demonstrate that when you look at how ethics are determined in a broader sense, the argument between the Hitchens about the ethics involved in the Invasion of Iraq after 9/11 for example, or the rise in antisocial behaviour and the degradation of basic manners and so on.....ethical egoism and utilitarianism are common forms of applied ethics, particularly individually. I don't think it is quite a clear cut as stating categorically ethics have improved, particularly since WWI.
No doubt if you are a staunchly Conservative Christian you will see things as getting worse as it is now less acceptable to practice your own prejudices and respect in your God has declined.
I am not even a Christian, let alone a conservative one and I can see the truth in what Peter Hitchens is referring to on a general level.
It all comes back to he same source and is all rendered pretty meaningless if the Christian god isn't real. Ditching medieval superstition in our law making and ethical thoughts should be considered a good thing.
I don't think it is meaningless if it gives a structured ethical system that informs and benefits society as a whole..if it were destructive then I would agree with you, I do not agree that it is.
EDIT:
In short, Christian ethics should be treated like anything else, man made, keep the good bits and disregard the rubbish.
You are preaching to the choir here as I am an advocate of Secular Law Making, but that is not the basis of the debate, which is not about whether individuals can be moral with or without God, but about Universal Morality and how we create authoritative structures to maintain that morality. Peter Hitchens suggests that without God then we are sooner or later caught out fiddling with it to suit our personal benefit and with God you are less likely to ignore the basic Universal principles as set out. I am not sure that it is entirely relevant in a society with a consistent strong rule of law, but I can see the truth of it in countries where there is no such social protections. God doesn't have to exist for this to be relevant, the people it applies to only have to think he does and that the consequences of their actions will be judged by such ethical principles.