As far as I know, if Tableau doesn't already have the lat/long for the UK postcodes, it won't plot on a map.
The way that I suggest is to find the lat/long for your postcodes online and create a custom geocoding file to import into Tableau.
Ensure you have no duplicates in your file and make sure it is a .csv (you can save in that format from excel).
Best of luck,
Eric is right that if Tableau doesn't have the postcodes already in the database then the best way is to use custom geocoding. However, it is also important to note that Tableau will only recognize the first segment of the 5-7 character code for UK postcodes (i.e. if it is any longer, it won't plot). It is also important that these codes are associated with the appropriate country.
Hope this helps!