Whether it's the "matting, seats, and stone" (3), the "neat organ" (6), or the "lectern" (13), lots of church-related objects come up in this poem. The speaker focuses on these objects because he lacks the spiritual knowledge to really understand how the church is supposed to make him feel. Nonetheless, there is something in all of these objects that attracts the speaker, even though he can't quite find the words to say what that thing is.
Line 3: The speaker says that these things are what make up "Another church," and these objects are pretty much the same no matter which church you go into. In this sense, the speaker is starting off the poem by devaluing the objects inside the church, robbing them of any holy uniqueness.
Lines 4-6: The speaker goes on with his list of the stuff that's inside the church. The mere listing of things keeps any one object from expressing its underlying significance. Referring to the flowers as being arranged in "sprawlings" shows that there's still a sort of chaos that infiltrates all of the church's attempts to take the natural world and arrange it into something pretty and meaningful. The speaker uses of the phrase "some brass and stuff" further shows his lack of respect for the meaning that these church objects are supposed to have.
Lines 13-14: As the speaker mounts the lectern, he casually glances at the holy readings that only a true believer is supposed to read out loud. The fact that these verses are in large print suggests that the worshippers reading these verses are getting old, and that no young people are replacing them. This foreshadows the decline of the church that the speaker will discuss in the coming stanzas.
Line 25: This line talks about how in the future, these holy objects might be contained in museum cases as reminders of what people used to, but no longer, believe in.
Line 44: The speaker asks if the last worshipper of Christianity will just be someone who's only interested in holy objects on a completely superficial level. Maybe this person will be a "Christmas addict" (43), who follows an irrational impulse to enjoy things like the smell of myrrh, and not actually interested in the church's deeper meaning. Here, Larkin might actually be critiquing the present-day people who are drawn to the church for this sort of superficial reasons. After all, there are a lot of people out there who only show up at church on Christmas Eve. Are we right, folks?