Green’s Dictionary of Slang

a lock-up, an early police station.

1822		Westmorland Gaz. 4 May 1/5: The two of them valiantly tok to their heels, leaving the prisoner [...] unable to toddle — to be grabbed by the charleys and warehoused in the roundy-ken.
1825		‘All England Are Slanging It’ Universal Songster I 39/2: I must pull you up, so toddle along with me; you shall pass the darkey in the roundy-ken.
1830		Egan Finish to the Adventures of Tom and Jerry (1889) 245: Unfortunate women, anxious to avoid a night’s lodging in the roundy-ken.
1833		‘The Chummies’ Society’ in Fun Alive O! 55: A pair of blue devils came in / And hiked us both to the roundakin.
1846		Swell’s Night Guide 71: I allays likes a chum, whether its on the tramp, or in a roundy-ken.
1848		Flash Dict. in Sinks of London Laid Open.
1849		Bell’s Life in Sydney 27 Jan. 3/1: Ven he reached the roundikin they inwiggled him in too .