I came here as a result of a Google search for "homey vs homely" because I saw a vlog on YouTube where the YouTuber visited her mother in a care home in Canada (which they apparently call nursing homes) and when she noted that her mother's room in the nursing home wasn't very homey, I got the same reaction you got when you saw the estate agent's client complimenting the property by calling it homely.

I was screaming at my mobile (in my head, not aloud) "don't you mean homely?" and of course, that's when I did the Google search to find out that the connotations between the two words are completely topsy turvy across the pond, which is the same as saying they're flipped at a 180° angle.

Here in the UK, someone who is homey is plain and boring, the opposite being a social butterfly or the life of the party. Homely is the word you want to use for a space that's warm and inviting.