Cornerstone by Arctic Monkeys, song analysis

A well known and loved song from Arctic Monkeys from their 'difficult' third album, but something occurred to me finally today. For a long while I thought this song was about a man who recently broke up his girlfriend, so he goes out to the town and starts transposing his ex onto other girls he meets in bars and clubs, but now I'm growingly convinced the narration centres around meetings with prostitutes. I paste the lyrics here: Thought I saw you in the battleship But it was only a look a like She was nothing but a vision trick Under the warning light She was close, close enough to be your ghost But my chances turned to toast When I asked her if I could call her your name I thought I saw you in the rusty hook Huddled up in wicker chair I wandered up for a closer look And kissed who ever was sitting there She was close, and she held me very tightly 'Til I asked awfully politely, please Can I call you her name And I elongated my lift home, Yeah I let him go the long way round I smelt your scent on the seat belt And kept my shortcuts to myself I thought I saw you in the parrots beak Messing with the smoke alarm It was too loud for me to hear her speak And she had a broken arm It was close, so close that the walls were wet And she wrote it out in letraset No you can't call me her name Tell me where's your hiding place I'm worried I'll forget your face And I've asked everyone And I'm beginning to think I imagined you all along I elongated my lift home Yeah I let him go the long way round I smelt your scent on the seat belt And kept my shortcuts to myself I saw your sister in the cornerstone On the phone to the middle man When I saw that she was on her own I thought she might understand She was close, well you couldn't get much closer She said I'm really not supposed to but yes, You can call me anything you want The original love for me seems also to be a prostitute, who has got out of the game or left town for some reason. 'Sisters' for me seems to be a reference to the sisterhood of local prostitutes, all the other prostitutes know the narrator, which is why most of them refuse the narrator's request to call them by 'her name' - it seems to be against the rules of the trade to let clients indulge in these kinds of fantasies. The narrator goes ahead and gets intimate with these women anyway, but not sexual but rather tries to be protective - he starts taking them home in taxis, with the only expression of his desire coming in his sniffing their familiar perfumes on the seatbelts after they had gone. Here I see a parallel to the situation described in When The Sun Goes Down on the first album, the narration comes again from the voice of a man who has fallen in love with a prostitute and starts empathising with all of them and wants to protect them. The final verse is where Turner provides the twist in the tale to the listener by making it plain that he is talking about prostitutes with the reference to 'the middle man'. He also makes it plain with 'I'm really not supposed to' that the narrator's frequent and repeated requests to indulge his fantasies is only possible when the pimp is not there and the girl is 'on her own.'