These may or may not meet your definition of a "simple dataset," but here are some online sources to check:
1) England and Wales -
The Ministry of Justice publishes Offender Management Statistics on a quarterly basis.
Current info: http://www.justice.gov.uk/statistics/prisons-and-probation/oms-quarterly
The most recent files: http://www.justice.gov.uk/downloads/statistics/mojstats/omsq-q4/omsq-q4-2011-prison-population-tables.xls
Previous info: http://www.justice.gov.uk/statistics/prisons-and-probation/oms-quarterly/oms-quarterly-editions
2) Northern Ireland -
It appears that there may be several editions of a Northern Ireland Office Research and Statistical Bulletin called something like "The Northern Ireland Prison Population" that may contain the data you seek.
Search for "prison population" on http://www.nio.gov.uk/
3) Scotland -
The Scottish Prison Service has this info.
If it is not on their web site (http://www.sps.gov.uk/home/home.aspx), ( http://www.sps.gov.uk/home/home.aspx ), presumably it could be requested as public information.