Green’s Dictionary of Slang

a fight, a tussle; cite 1849 poses this against a fight that includes biting and kicking.

1824		Pierce Egan’s Life in London 17 Oct. 6/2: Coachee [...] began pulling off his coat [...] saying ‘come, I’ll have an up and down or two with you, my covey!’.
1840		Era (London) 18 Oct. 5/4: He said, ‘Now then, old tar, when you and I have had an up and a downer, we’ll talk about this matter,’ [...] ‘An up and a downer?’ [...] The defendant: ‘Why, I scrapt him, your worship.’ — Alderman: ‘Officer, please explain what is the meaning of scrapping him.’ — Officer: ‘He means, your worship, fighting’.
1849		Paul Pry 23 Apr. 2/1: As soon as it is settled that they are to fight, a ring is formed and the combatants agree whether it is to be ‘upe an’ dawn’ or not.
1866		Sportsman 25 Oct. 2/1: Notes on News [...] [D]evices worthy of the bystanders at Lancashire ‘up and downer’.
1927		Daily Tel. 6 Sept. 7/7: We has a bit of an up-and-a-downer last night, and he has the cheek to fetch a policeman.
1935		G. Ingram Cockney Cavalcade 143: He used to be one of the best in the Nile at an ‘up-and-a-downer.’.
1956		J. Curtis Look Long Upon a Monkey 63: The coke shovel was damn handy in an up and downer.
1981		J. Sullivan ‘Cash and Curry’ Only Fools and Horses [TV script] So Mr Ram you and this, er, Vimmel, you’ve been having a bit of an up and downer then have you?