Yes, you absolutely 100% are. You could sell your London home, move to that village, and live off the proceeds.

Saying you aren't wealthy because you happen to live in your biggest asset is delusional (and part of a dominant political narrative promoted by the homeowner class).

Consider what would happen if a major financial bill struck each family (like, $500k). The London family might be forced to sell their flat and move into an apartment (or move out of London). The village family would lose everything they own and still be in debt.