Green’s Dictionary of Slang

blow-through n.

[SE blow through, the process of blowing steam through the cylinder of an engine etc, to clear it of air]

an act of sexual intercourse.

[UK]K. Amis letter 19 Feb. in Leader (2000) 505: Wouldn’t give a pinch of shit for his chances of even an occasional blow-through.
[Ire](con. 1940s) B. Behan Borstal Boy 175: For his morning blow-through.
[UK](con. WWII) B. Aldiss Soldier Erect 132: She was good enough for a blow-through.
[UK](con. WW2) T. Jones Heart of Oak [ebook] The next place we called at was Aden, / The girls wouldn’t fuck but we made ’em; / Ten dollars I’d pay for a blowthrough each way [etc.].

In phrases

have a blow-through (v.)

to have sexual intercourse.

[UK]Partridge DSUE (1984) 100: C.20.
‘MommaKin’ Forum 25 Jan. [Internet] have a bit on the fork / have a blow through / have a brush with the cue.