UK (London) - how long are the waits to be placed?

I am a 20F female fleeing DV and have been living in a hotel for the past couple days. I spent the whole of today calling up refuges with no success and was put on a waiting list for 2.

I will enquire v soon ab emergency accommodation with my council but I want to know how long on average I can expect to wait to be housed in a proper refuge? I know as a single woman with no children or special, complex needs I am lower on the priority list.