Thanks to everyone for their comments re finding a housemate :-).
Someone came to look at the room yesterday; since she has decided to take it, I am going to call her 'Paula'. She seemed relatively normal, despite wearing very pointy shoes and a tweed jacket, which scared me slightly. Despite that, she brought up things like money; cleaning; bed-linen; where the nearest shops and take-outs are etc. etc.; all of which lead me to believe that she would make a good lodger.
In addition, she didn't smell, and she didn't have any scary twitches or apparent psychoses.
Also (and this is what really endeared me to her) she didn't mind the cats.
Obviously, we have put in the advert that we have two cats. However, B and I went away for the weekend, and due to an oversite, I left the cat-flap set to 'in only'. It is one that opens with a magnet attached to the cats' collars and you can also lock it for access in various combinations. We have been having a tom-cat visit and leave smelly calling cards in the kitchen, so I have been locking it at night; on Friday morning, I must have clicked the locking-wheel to the left rather than the right.
Result: two cats who had spent forty-eight hours locked in the house.
They greeted us with the usual yowls and happy dances when we came home ... but then B noticed that they had been pulling at the carpet to try to get out the front door.
And then I noticed that they were sitting by the back door, crying plaintively.
And then I noticed the smell in the sitting room.
It could have been much worse. And under the circumstances, I suppose that I am thankful that we have a couple of very large house-plants. Even if I am going to have to re-pot them both next weekend.
So, as Paula arrived only about an hour after we got home, all it needed was for me to put a nice pan of sprouts on to boil and don some fluffy mules and I could have started a new career as a slightly seedy boarding-house landlady.
I explained the situation, emphasising how little trouble the cats were and that they were usually models of feline decorum; only to take her upstairs to see the room and to find one asleep on the bed and one on the windowsill. Both shedding enthusiastically.
Despite all this though, (or, more worryingly, perhaps, maybe because of it) she wants to take the room until the election, as she is an assistant to a local MP and is normally based in Westminster. She has taken it for five weeks, ending on May 7th, and can provide both references and a bond.