Just wanted to update this thread in case anyone finds it in the future.
There doesn't seem to be an organisation in the UK who can organise dog visits to private homes. The closest I found was
http://animaldaysout.com/ who suggest they can on their website but didn't seem hopeful when I spoke to them. So I was dreading having to explain that there wouldn't be a dog any time soon.
In the meantime, last weekend there were some other issues which meant I had to organise 4 weeks of respite care in a local home urgently. I've just got her in to a nice place not far away and the best bit is that they have dogs visiting regularly, which my mum is over the moon about and although she was very reticent to consider a home before, I'm wondering whether the promise of regular dog visits will actually change her mind about care homes. She even told me she hated her house the other day, so I wouldn't be surprised if when she comes out she'll be begging me to go back in there permanently.
Funny how things can change so quickly!