Postcode filtering for WooCommerce with proximity feedback

I have a WooCommerce project that user the Webkul Multi-Vendor Marketplace plugin. I need to replicate the functionality from Just Eat where a user enters their postcode and then are taken a page with a series of results of vendors that will deliver to that location. I do not have time to write this part of the project but I know how I'd like it done. Part 1. The delivery postcode are stored against the user profiles, which have ACF fields for delivery postcodes, e.g. Restaurant A delivers to SE1, SE2 SE6 and SE7, but nowhere else. The results loop needs to reflect this, only showing restaurants that will deliver to the customer address. The postcode needs to be stored as a session cookie that persists throughout the site so if they change category their postcode is remembered and for any future visits. Part 2. Additional functionality is also required to show a proximity distance from vendor stored address to the customer's postcode. i.e. 0.2 miles, 5 miles etc. This will need to be displayed in the category loop results. More information available upon request