Green’s Dictionary of Slang

the fourth round of a pub drinking session.

1936		M. Harrison All the Trees were Green 271: Refusing an invitation to drink a ‘final’.
1938		Sun. Dispatch (London) 3 July n.p.: Publand...first round is known as ‘one’, second as ‘the other half’, third as ‘same again’, fourth as ‘a final’, fifth as ‘one for the road’, sixth as ‘a binder’, and seventh as ‘swing o’ the door’ [DSUE].