The poem does change in tone, but the shift occurs earlier than in the line you cite here. Consider it in context:
Ne'er saw I, never felt a calm so deep!
The river glideth at his own sweet will:
Dear God! the very houses seem asleep;
And all that mighty heart is lying still!
These are the final lines in the poem, and for the first time in the poem, the exclamation point has been employed, indicating a change in tone.
From the beginning of the poem until these concluding lines, the speaker has described the beauty and serenity of London as it appears to him in the early morning hours. It is a city asleep; the air is clean and the city is quiet. He describes it as an extension of nature itself, as it is "Open unto the fields, and to the sky." The tone is one of quiet reverence.
In the final four lines, however, the tone changes. The speaker is no longer merely an observer; he has been drawn into the moment. The peaceful calm of the city has infused his spirit; he, too, now feels serene. Thus "Dear God!" expresses his joy and wonder in the experience. His feelings are so all encompassing and profound that every part of the city, even the houses themselves, affect him. Every part of the "mighty heart" of London exists in a state of peace, reflective of his own.
An interesting feature of Wordsworth's poem its subject. In Romantic literature, spiritual experiences are most usually inspired by nature. In this poem, London is presented in these circumstances as being more beautiful and awe-inspiring than nature itself.