Install this plugin for UK address validation on Zen Cart registration page, checkout pages and Admin/customers page from 3x Software & Royal Mail.
Sign up for a trial account that includes 30 free credits at www.postcodes4u.co.uk.
Enter the username and the product key generated from the www.postcodes4u.co.uk site into the /postcodes4u.php file and have address validated data for your customers orders.
After the trial period (30 credits) has expired, it's easy to purchase more credits from a range of competitively priced bundles to ensure your dispatches are going to a UK address that has been PAF validated.
See this plugin in action on our demo Zen cart site, just select United Kingdom from the country drop-down
(Tested in v1.5.7)