A month for council to repair toilet?

My toilet hasn’t been flushing since yesterday. It doesn’t refill. I am a social housing tenant and they told me that the earliest appointment they can give me is 4th February.

Is this legal? Is this acceptable?

They told me it’s not an emergency since I can pour water down the toilet to make waste go away, but I don’t think this is very effective plus the sound of the toilet trying to refill is highly disturbing at night when trying to sleep.