Is there any service to convert a UK postal code to a city name? Does one postal code always map to one city, or to more than one? Is there a free web service to do this conversion for me?
Try using Bing Geocoder, I believe they do UK, so you should be able to look up the coordinates of the zip code and in the results you will see the cities that correspond globally to that zip code...
P.S., Don't use google geocoder for UK, it doesn't work properly from personal experience.
Mapsdata and other similar services allow you to load up Postcode and attribute data in .xls or .csv format for free and then view it on a map if that's the end product that you're looking for.
Here's a wiki description of how the postal code system works using the first or first and secondary alpha characters. It's regional specific and not city, ie PH is the administrative district of Perthshire which also contains the city of Perth.
The Ordnance Survey is also a good resource on this.