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OSM does not support post code search but please note if you have OSM active on your device and also have one of the maps previously listed you can still do a post code search even though the other maps are not active.
Like so.
I have never found the need to do a post code search, you can either use the address function, map point function or send the address as a waypoint to the device as a gpx file.
A bit of a kludge but do a post code search in google earth . make a placemark, export as kml use gps vizualizer to convert to gpx, send to device. It will be added as a "location".
For the uk either city navigator europe or GB discoverer.
http://www.handtec.co.uk/garmin-city-navigator-europe-nt-010-10680-50.html