I think I can tentatively say, it's sorted.
This is how it happened. The sermon yesterday was on Matthew 6 v 24-35. "Therefore I tell you, do not worry about your life, what you will eat or drink; or about your body, what you will wear. Is not life more important than food, and the body more important than clothes?" (v25) Afterwards, there was prayer for people who were worrying about things and needed to trust God. So I went up for prayer and rattled off a list of things I was worried about, including having nowhere to live in a month. One of the women praying for me said "I'm looking for a housemate". She's someone I know vaguely, having met once or twice before. So they prayed for me and I felt better and then we talked about the house. After lunch, I went and looked at it. So many things are just right. It's in the area I wanted to live in, down the road from more friends from church, the rent's right, there's a gas cooker (little thing really, but I do like cooking on gas), there's a garage I could keep my car in (luxury as far as the bug's concerned!), plenty of book shelves, the timing for when the current occupants are moving out is right. God's good!
It's not completely finalised yet, I've got to speak to someone at the letting agents to start the official paperwork side, but looking at the way it's all just come together, just at the right time, just right, I think it's going to be OK.