As fo3nix has indicated, full postcode maps are only available on a commercial basis.
However, if you only need to know a few local postcodes, you can use the Royal Mail's postcode finder. It only allows you to perform a maximum of 12 searches per day but it might be of use to you:
http://www.royalmail.com/portal/rm/postcodefin der
Here are a couple of hints:
1. It's possible that the postcode finder might check how many addresses you've tried by setting cookies on your PC. Try deleting your cookies (or looking for the relevant ones and just deleting those) and you might be able to carry out unlimited searches.
2. Most roads only have a single postcode. (e.g. 23 Acacia Avenue will have the same postcode as 46 Acacia Avenue). Only very long roads will normally have more than one postcode. (Sometimes this is different for 'odd' and 'even' addresses but, more usually, different lengths of the road will have different addresses).
Chris