Nature comes up in lines 26 and 36 to show how the natural world might take over the church buildings once the last of the human believers have gone away. There's a certain inevitability to this that also gives the image a post-apocalyptic vibe, showing a world where humans are no longer in the picture. To "let the [church] rent-free to rain and sheep" (26) suggests that there is a power to the natural world that is beyond human attempts to feel significant. The universe might actually be a cold and uncaring place, and religion is an attempt by humans to force some sort of cosmic meaning onto it that isn't actually there. Religion is also supposed to make the natural world into a meaningful place for humans, but here we only find images of "Grass, weedy pavement, [and] brambles" (36) taking over the church, breaking down our attempts to preserve a sense of higher meaning and purpose.
Lines 4-5: The mention of flowers at this early stage in the poem is playing on the aura of religious celebration and hope that flowers traditionally symbolize, but in this case the flowers are strewn about in "sprawlings," which gives a sense of lost order, confusion, or desperation. The flowers have also gone brown, which underscores the same type of decay that the speaker thinks might happen to religious faith in modern society. Moreover, appealing to nature here shows how nature always decays, and human efforts to make nature into something meaningful and beautiful are artificial and destined to fail over time.
Line 26: Like the flowers that have gone brown, this image suggests that the church (and the meaning it tries to create) might not be able to stand up to the natural world in the long run. This image of rain and sheep entering the church even has a post- apocalyptic feel to it, as if humans are completely gone from the Earth. This again shows that human efforts to make the world into something meaningful and familiar might actually be fighting a losing battle, since everything that we create (whether it's spiritual or physical) will eventually decay.
Lines 35: Again, a stanza ends with an image of the natural world overtaking the church.