Green’s Dictionary of Slang

(UK Und.) a style of walking seen as denoting a habitual criminal: the walker takes short, cramped steps, learned in the exercise yard of a prison where prisoners walked in close single file around a circular path .

1959		J. Gosling Ghost Squad 41: I said: ‘I’m not coming in here with you again. You embarrass me.’ He raised a surprised eyebrow. ‘The Brixton Shuffle!’ I said. Tommy was not amused.
1978		M. Goulden Mark My Words! 189: This institutional aura is as easy to detect as is the ‘Brixton shuffle’ which characterises the gait of a man who has been ‘inside’.