It all depends on what band you are in, how many bedrooms you need, and what you bid for. If you are in the top banding, Band 1, you could potentially wait a few months to a couple of years. If you are in Band 2, you wait anything between 1 year and 60 years (unless you are homeless then your wait time could be less). If you are in Band 3 you could wait anything between 4 years and 137 years (unless you are in Band 3 sheltered or homeless then your wait time could be less). If you are on Band 4 you could wait anything between 10 years to 150 years.
If you place restrictions on what you are prepared to accept, your wait will be longer than average. For example, if you bid only for houses and not for flats, only in private roads and not on estates, only for council and not for housing association homes, or only for 1-beds and not for studio flats, you will wait a lot longer because you are competing with more bidders who are also attracted to these kinds of home. The more bedrooms you require the fewer properties we have available. If you need disabled adaptations you may have to wait some time for a suitable property to come up, even if you have been put in one of the top bands.