I think back in the day this may have been easier. Now it is difficult to sell a home and you may need all the advertising etcyou can get.
We are currently selling a house. Although we have 2 estate agents, we were approached privately by a couple. We didn't end up selling to the couple, but I found the whole process a bit awkward. Though I'm sure it could have been done. But at the end of the day, they only knew we were selling from the Estate Agent's signs..
We are now going through the sale process through the Auctioneer and although it's easy money on his part, I prefer the distance from the buyer.