Royal Mail is another very popular main service in the UK. This plugin provides shipping rates to your store without the need for any API. In order to use this plugin, you need to set currency to GBP and United Kindom as the base country. Though this plugin does not provide many features to your store, as there is no public API available for Royal Mail, but if you are using Royal Mail, then this plugin will certainly help you a lot.
This is the EXACT same plugin as distributed by the developer on WooCommerce. The developers’ links are provided above.