One of my Professors (semi-)recently published an opinion piece on this very subject (morality without religion) in the New York Times.
Interestingly, there are also people who would argue that the difference between us and animals is a matter of degree and not of kind. People like Evolutionary Ethicists would say that any animal could, in principle at least, evolve a moral sense. I think most would agree that humans are the only known moral creatures, so in that sense we would have a "moral compass" that animals lack. But this would not be because of any thing essential to humans and exclusive to other animals (like a "soul" or what have you), it would just be something that we acquired due to evolutionary forces that could very well induce the same "growth of a moral compass" in other creatures.
Now, to the more historical bit of your question. You can read a good summary of Hume's views on religion at the Stanford Encyclopaedia of Philosophy (this should be your substitute for Wikipedia on all things philosophy related; the articles are all written by top experts in the field and are generally quite exceptional), section 9 should be exactly what you're looking for. Especially relevant:
On this view of things, God and a future state are wholly unnecessary for moral life and human society. The relevant foundation for moral life and conduct rests with the key elements of human nature that we have mentioned — pride, sympathy, moral sense, and conventions. Moreover, the psychological mechanisms involved are strong and steady enough in their influence to ensure that there exists a reliable correlation between virtue and happiness and vice and misery. By these means, we find that human beings are constituted in such a way that they are capable of moral conduct and able to sustain social cooperation and harmony. In so far as religion plays any role here, Hume maintains, it is more likely to corrupt and disturb, than to contribute, to morality or social stability.
As to Russell, this article on his moral philosophy has some relevant stuff. From section 2:
Russell was much exercised by a problem that also bothered Sidgwick: the Dualism of Practical Reason. (See Sidgwick (1907): 496-516. See also Schulz (2004), ch. 4 in which it becomes abundantly clear how very preoccupied Sidgwick was with this problem.) According to Sidgwick, it is rational to do what is morally right (by maximizing pleasurable consciousness on the part of all sentient beings) and rational to do what is prudentially right (by maximizing pleasurable consciousness on the part of oneself), but, when the two come into conflict, the one does not seem to be any more rational than the other. If God exists, then He can ensure that it will pay in the long term to promote the public interest, by rewarding the righteous in the life to come. What is morally right will coincide with what is prudentially right, and that, consequently, is what Practical Reason will command. But if, as Sidgwick was reluctantly inclined to think, there is no God, what is morally right and what is prudentially right will sometimes come apart, and Practical Reason will speak with a divided voice. If it does not always pay to be good, then it is not clear that is more rational to be good than to be bad, a conclusion that Sidgwick found deeply disturbing. The rather priggish young Russell was bothered by the problem too (a solution, he said, would be ‘a real solid addition to my happiness’) because, like Sidgwick, he did not believe in God.
Another place you might look are in various scattered Russell essays. For instance, "Am I an Atheist or an Angnostic?". His lecture "Why I Am Not a Christian" is probably the most popular statement of his views on religion. It contains a section on the "moral arguments for Deity". He actually gives something similar to the famous Euthyphro dilemma:
Kant, as I say, invented a new moral argument for the existence of God, and that in varying forms was extremely popular during the nineteenth century. It has all sorts of forms. One form is to say there would be no right or wrong unless God existed. I am not for the moment concerned with whether there is a difference between right and wrong, or whether there is not: that is another question. The point I am concerned with is that, if you are quite sure there is a difference between right and wrong, then you are in this situation: Is that difference due to God's fiat or is it not? If it is due to God's fiat, then for God himself there is no difference between right and wrong, and it is no longer a significant statement to say that God is good. If you are going to say, as theologians do, that God is good, you must then say that right and wrong have some meaning which is independent of God's fiat, because God's fiats are good and not bad independently of the mere fact that he made them. If you are going to say that, you will then have to say that it is not only through God that right and wrong came into being, but that they are in their essence logically anterior to God. You could, of course, if you liked, say that there was a superior deity who gave orders to the God that made this world, or could take up the line that some of the gnostics took up -- a line which I often thought was a very plausible one -- that as a matter of fact this world that we know was made by the devil at a moment when God was not looking. There is a good deal to be said for that, and I am not concerned to refute it.
Later on in the same lecture is a section entitle "The Moral Problem" where he discusses how religion and morality seem to conflict.
Well that's about all I know on the subject/can find resources for in a quick scan. Enjoy!