You can access the properties via the WordPress REST API by visiting the below URL:
https://{your-site.com}/wp-json/wp/v2/property
You can filter the properties returned by passing in the same parameters as used on a standard property search on the website. For example:
https://{your-site.com}/wp-json/wp/v2/property?department=residential-lettings
https://{your-site.com}/wp-json/wp/v2/property?department=residential-lettings&minimum_bedrooms=2