Japanese friends hesitate at the door when you invite them in as if they don't quite know what to do. They may have noticed that you are wearing slippers, and wonder if they should take off their shoes when coming into your house, as in Japan. You need to assure them that it is OK to walk on your carpet in outside shoes- after using the door mat!
Maybe it is not OK to walk on this English person's carpet in outside shoes? There may not be many Japanese folks who wear shoes at home, but there are a few of us British people who do not like people wearing shoes in our homes.
Even if one did not mind shoes walking on one's carpet, I think perhaps a better approach might be to say 'Feel free to take your shoes off.' The Japanese person might feel more comfortable and at home after removing his or her shoes.