In my experience, the best way to sell a property is normally ask the neighbours, because they can either but it to swap homes or expand theirs, or know someone interested (and they vouch for the neighborhood!). So, if you know them, invite them over and show them the house because they might know someone. If you don't know them, go meet them right now!

If the prime minister is around, I guess he knows someone that is in his inner circle, with money and that wants to live near him, in an AWESOME home.

good luck