Filter/search widget for collection items based on a UK postcode

My client has a Webflow Collection that contains physical locations across the UK. There are fields for geo co-ordinates (Latitude and Longitude), and a text field for the address. (Separate postcode field could be added in necessary)

They now would like a widget on the homepage to be able to search for “locations near you”, with a field for visitors to submit a UK postcode. They’d then be taken to a page where the closest locations are listed.

I have no idea where to start or how to approach this. The only thing I assume is that this will need substantial custom coding. What approach would that take?

Thank you for any advice.