The housing market is not a perfectly competitive market as it fails to fulfil the necessary characteristics of a perfectly competitive market.
Firstly, in a perfectly competitive market, all the products are homogeneous, meaning they are all identical. this is clearly untrue in the housing market as houses are not all the same, they vary in size, location, quality and many other areas. Therefore, the condition of homogeneity of products is not fulfilled in the housing market.
Secondly, a perfectly competitive market means buyers and sellers both have perfect knowledge. This is not true for the housing market. Sellers will often know more about the house they are selling than the buyers. Buyers will usually do a lot of research into the house to increase their knowledge, but they will never have perfect, complete knowledge about the house they are buying. Therefore, this condition of perfect competition is not fulfilled either.
There are other factors of perfect competition that are also not present in the housing market, but the fact that he two factors explained above are missing already implies the housing market is not perfectly competitive.