Hi gmw. Here's a pile of line edit comments. As always, take whichever make sense to you.
Spoiler:
She leaned forward. Gavin liked that. "What do you suggest?"
This is just slightly confusing enough as to who is speaking to break the flow, since Gavin is mentioned just before the spoken dialogue. Even just breaking her dialogue onto the next line would help.
"I got a thing for the fifties," Gavin continued. And he does.
Should this be 'And he did'? In the next sentence you write, 'but he loved old fifties stuff'.
"Not the cheap kitsch they sell these days," he explained, in case she got the wrong idea, "the good stuff."
My gut feeling is that it should be "The good stuff." I think if you didn't have the attribution in the middle, that would have been, "Not the cheap kitsch they sell these days. The good stuff."
There were only four apartments up here.
Gavin waited for her to close the apartment door behind them
Two uses of 'apartment' very close to each other, with two more only a paragraph later, then three in the same paragraph a little way further.
Gavin guessed the man was in this forties somewhere
Typo. Should be 'his' forties.
It was set up for a man, there was no sign that a woman lived here
While I'm mostly happy with your use of commas to divide what could be cast as two separate sentences, this one does bother me, and I'd prefer it separated with a period. It really felt like the first part was emphatic. 'It was set up for a man.'
except that it was very tidy
I'm not sure this will work for all readers. I'd have believed 'except that it was very clean' better. I've generally found men living alone to be tidier than women.
but this was getting creepy. "I'm getting out of here," Gavin said
Two 'gettings'.
Cooper grasped him by the arm, it was a strong grip.
Another slightly jarring use of the comma. Perhaps consider a semicolon, or breaking it into two sentences, or, 'Cooper grasped him strongly by the arm.'
"Exactly, What?,"
It's not instantly clear that he's changing 'Twat' to 'What', and the question mark immediately followed by the comma looks odd. I think this has to be punctuated either as "Exactly. What?" or "Exactly. 'What?',"
"Yeah, right. Pull the other one, it plays Jingle Bells." Gavin snorted into his glass.
Does he snort after saying all that? Consider flipping the attribution to the front?
"This place?" Gavin asked, he wasn't totally out of it yet.
This felt a little odd. Consider, 'Gavin asked, not totally out of it yet.'
door closed the prick starts ranting. Vera tried to soothe him
'starts' and 'tried' feel wrong so close. It feels to me that the tense should be consistent here, even though this is reported speech. The rest of this is in a past tense, so I feel that 'started' would be better.
that first night's are special
Misplaced apostrophe. Should be 'first nights are special'.
Gavin asked, his tongue seemed
This is another one where I'd prefer a period instead of the comma. In this case, because the second clause could genuinely be a continuation of Gavin asked, but would be worded differently if so (as something like 'Gavin asked, his tongue seeming to to have trouble').
He realised his eyes were closed and wondered how long they had been like that.
I think this needs a 'he' before 'wondered'. (At the moment it's the eyes doing the wondering.) Or possibly just add a comma after 'closed'.
He called her Sophie and frowned slightly, that wasn't the right name.
The comma use jarred for me here too. It's too important a part of the story to risk that. Please could you consider using a period, or adding 'as', or even using an ellipsis here instead of the comma? The ellipsis would also support the feeling of going under.
and stain the lounge.
My reaction was 'the whole lounge?' Perhaps consider 'the carpet' or 'the couch'.
to be more careful not to let his impatience
Do you need the 'more'?
If you didn't give them enough of the truth then it, whatever it was, didn't take, Vera would fade and you had to start all over again with another one, and sometimes it took a month or more before the itch would come back.
Long sentence. Perhaps consider a period before 'Vera'?
for quite a small fee
Do you need the 'quite'?
would remember anything of this place then, some did.
For me, this would make sense more immediately with an 'as' before the 'some'.
I'm a con man and the thief
Typo? Should that be 'a' thief?
Graham