Impossible angel

[artjewl]

Impossible angel

Beer and cigarettes - Interesting and effective line break
and you, your languid locks, - languid is appropriate, and the alliteration is well played, continuing to the next line in always -- the "L" sound itself is a slurring.
are always in my world of drunken walks
through Barbican and Bishopsgate,
in the moonbeam shallows
of walls spattered with poetry.

Thursday nights your longing is a sea - if you intend to liken "Thursday nights" to "a sea crossing" (as you mentioned in another comment), are you addressing Thursday nights? Do you mean to say "Thursday nights, your longing..."? or do you intend to say "on Thursday nights..."? Also, if you mean for crossing to be a noun, I really think you need to keep it with "sea." 
crossing through hours of drunkenness.
Mindful glances in the mermaid shadows
turn not to me. - At this point, I'm not yet convinced that the inversion is right for the previously established tone...

Impossible angel -wonderful pairing
that runs not to me. - ...but the repetition helps me buy the inversion.

But runs to the deep sea's emptiness
in the white frothed wave that follows - I think "white frothed" should be hyphenated.
the moon's pale lamp of loneliness
that burns not for me. - 

Overall, I find this to be a beautiful piece in which alliteration enhances the lyrical quality. The line breaks are strong and help to underscore the imagery. I think it's nearly done -- it just needs a little clarification.