Shiptheory doesn't address validate things and Royal Mail's OBA API doesn't either.
So if the postcode is valid, (e.g. format looks correct) it doesn't check that the first line matches the postcode which is really common for various reasons. Have you ever type in an address on a Satnav and it's a new building and it's not there? That's the reason lots of carriers don't do address validation, it tends to cause issues not accepting shipments for addresses that are valid, but haven't been updated on the various address databases.
However if you really want address validation, your best place to implement this would be on your checkout(s) on your webstore(s). We don't specifically recommend extensions, however there's a bunch available, one example is: https://craftyclicks.co.uk/plugins/download-info/magento/. As I mentioned, we don't endorse this extension, but it's out there and available. And this extension only works with Magento. If you're using a different sales platform, please check if they have an extension that does address validation.
Any other questions or concerns, please don't hesitate to contact support.