SW unwilling/scared to make this decision.
So sorry to hear about your mum :-(. Unfortunately, I don't think any of the authorities are willing to make a decision. At least, that's my experience too. I'm in a similar situation to the OP with my dad (he's in a care home and often says wants to go home, despite the obvious difficulties; the house stands empty and needs to be sold).
So I rang the Office of the Public Guardian - they have a helpline number on the documents - and thought they might help. The advice was that dad's dementia diagnosis goes 'some way' to deeming him incapable of making his own decisions. Some way?! I didn't specifically ask about a capacity test, but neither was it mentioned, and the whole conversation was quite 'woolly'.
In my case, I've written down all the concerns I would have about dad returning to his house with as much evidence as I can think of as to
why these would be a problem. For instance - stairs and stairlift (inability to use one); how he might cope in an emergency; evidence of leaving house unlocked, responding to door-steppers etc; lack of self care being beyond the scope of care visits (in my opinion); general support needs and vulnerability. I've signed and dated it. I'm now thinking of getting social services involved again, since dad's insistence about 'going home' is becoming too much.
I know our situations are different but I thought it might help to share this, since this thread has been a great help to me!