Who cares if its cheeky? Its your money I think a lot of people are too concerned about offering too littele and thereby appear cheeky. In a way you are being too nice it is a financial transaction at the end of the day.
Would you pay (and this goes to anyone in a similar situation) €20,000 for a car from a dealer if you thought you could get it for say €17,000, just as an example? More people have to start thinking like this or we'll keep paying ridiculous amounts for housing which is a basic need (maybe not a a necessary purchase, i.e. people could rent).
Housing is (I think OECD said by 15% or it could have been more, correct me if I am wrong someone) way over valued in this country. Would you pay way over the value for other products in a shop?