Hi there JP, 
Welcome to OSM.
Unfortunately Royal Mail's find a postcode service's terms and conditions is not compatible with OSM's license and as such it cannot be used as a source when mapping. 

With the addresses, the correct way to solve this situation is with the addr:parentstreet tag but unfortunately the web editor doesn't display a field for this tag. 

I've fixed these issues for you. 
Kind regards,
Kits.