Brooke devoted a chapter to Paley's approach to natural theology, and its popularity in Britain in the late 18th and early 19th centuries:
The point is not that science undermined the design argument -- certainly not in the eighteenth century. Quite the contrary. It was that religious apologists were asking too much of it. A religious burden was placed on the sciences, which they were eventually unable to carry. This overburdening can be seen in the contrasts between the style of natural theology presented by Paley and that to be found in earlier paradigms of Catholic and Protestant theology. Severe limits had been placed on the scope of natural theology by Thomas Aquinas and, at the Reformation, by Calvin.Brooke goes on to point out that Paley's approach was bound to be vulnerable, as indeed it turned out to be. Darwin started as much a fan of Paley's natural theology as any other naturalist of the period. But his work undermined it fatally. I think it was Edward Oakes S.J. who once quipped it was too bad Darwin hadn't studied Pascal instead of Paley when he was in school, theologians since that time might all have been spared a lot of grief.
[...]Nor would Aquinas have countenanced the facile procedure whereby divine attributes were gleaned from nature, independently of revelation. In fact, he is associated with the saying that we know of God rather what He is not than what He is. This refers to his so-called negative way of approaching the nature of God. By successively denying him the characteristics of finite things, such as materiality and mutability, a knowledge of His attributes (albeit in a negative sense) could be gained. It was a far cry from that position to the position of Paley's claim that God's caring nature could be discerned in the hinges on the wings of an earwig. (p. 195)
My own feeling is that Aubrey Moore was right when he wrote in 1891, "Darwinism appeared, and, under the guise of a foe, did the work of a friend."