Good luck with this and i hope that your relative is not kept waiting much longer. I had to do this for a relative who was looking to get housing and i know what this can be like.

You have to make sure that your relative has priority in one of the areas at least that council specifyor you will get no where for years. Get doctors letters and send them to them if you have not and let them know how bad the situation is making your relatives health.

Maybe your relative will need to go on the homeless
register. If they are living with somebody they could maybe take in a notice to quit to the council. They may get put into bed and breakfast this way but it could lead to them maybe getting housed quicker. This is not a route that everybody can take though or would like to see a family member go through.

Even doing all this you could be waiting at least a year or so on the waiting list. There are a lot of people in desperate situation out there all needing help and some people have been waiting for years.

Good luck though and i hope that your relative gets to have their own place soon.