The Home Office publishes data on the number of arrests in the South Yorkshire police force area. These data include the total number of arrests, and breakdowns by gender, age, and ethnicity of the person arrested, and the offence type that they were arrested for. These data are all published annually, and the latest data, which cover the year 2013/14, can be found here:
Data for previous years can be found here:
The Home Office does not hold data centrally on the number of arrests made in parliamentary constituencies, or individual towns or cities.