Here´s the best site on the net I found on Cromwell tank`s history...
http://freespace.virgin.net/shermanic.firefly/a27m.html
according to it :
It only served in North West Europe (at least in WW2) and was not used in Italy, nor in the Middle or Far East, baring a few test vehicles, until after WW2. Post war it saw action in Korea and soldiered on as a training tank, until at least 1960. Exports seem few and baring use by the Poles and Czech's under British leadership it was not used by foreign nations, except for the odd test vehicle, like the one shipped to the US for comparative trials. The one exception would seem to have been the single one captured in Korea from the British and then used against them, until the Cromwells grandson (the Centurion) took it out with a well placed 20 Pdr shot.