Hi,
I've tried an install of 1.3.8a with the UK Zen Cart Template.
Only my second install of Zen Cart, so I could have made a mistake but I think that I followed the instructions carefully:
NEW INSTALLATION INSTRUCTIONS
1. Upload your Zen Cart 1.3.7 files to your server but do NOT run the installer.
2. Upload the contents of the folders in the UKZC-1.3.7.base file (admin, includes, zc_install) to your server.
3. Now run the standard Zen Cart installation.
In your browser, enter the URL to your new shop, and the Installer should automatically start.
Example: http://www.mydomain.com/catalog
- or - to start the installer directly, use: http://www.mydomain.com/catalog/zc_install
NOTE: You will now have the opportunity to set your UK county during install 
- Thanks Dr Byte!!
4. Log in to your admin area.
5 Select : Configuration -> Shipping/Packing - select post code - edit - and add your post code.
7. Select : Localisation -> Currencies - and press the 'update currencies' button. Check the "default" currency is set to GB Pounds
8. Finally to bring it together select : Tools -> Template Selection - Click on Edit and choose either 'UK Zen Cart Default v137' or 'UK Zen Cart Classic v137 Std'
I couldn't see any UK counties to enter into Zone and after installation the dates (eg. 05/21/1970) are still U.S. format. The UK templates were not available to choose.
It looks as though the sql didn't run - I ran it manually in phpMyAdmin and it ran OK. I now get the Counties, the prices are in GBP.
The extra files included in your download weren't copied to the correct places so I did that manually and it now appears to be OK.
So overall it looks as though the files and the SQL were correct just that they weren't run by following the current instructions.
Hope this helps, thanks again for creating the code,
Chris
PS In instruction 3 above it didn't work with '/catalog'.