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Hi, Lottie! Sorry it's taken me so long to post this update; my net has been crashing all day! :(
Well, I collected my tools: the teddy, hot water bottle and clock and went over for the night. We didn't fuss over him when we got in and at about 10 o'clock he came out from under the sofa where he'd been all day and jumped up. We sat as still as we could as he's always been very jumpy and he explored behind the cushions and after a while we decided to try him with the piece of string we had and he was so playful! After that he was all over the flat having a good nosey.
We had planned to put Oscar in her smaller second bedroom for the night with everything he needed, but once he was in there he was crying like he was being killed (drama queen!), so we let him straight out (can't upset the neighbours again!). I set it all back up in the living room and slept on the sofa. When I first turned the lights off (with the telly still on) he did start crying quite a bit, but they weren't as desperate as they've been before. He was quiet after a while, though, and only woke me up a few times in the night with short bursts of miaowing. Not too loud, but he seems to adore the sound of his own voice; he even does it when he's eating and drinking and it sounds like he's gargling. :)
He didn't come to me during the night, but during the evening he was leaning into my hand when I stroked him instead of pegging it, for once. :)
He didn't go near his bed, the cat carrier (which I left open with a blanket in), or his surrogate mummy (teddy, hot water bottle and clock), so I don't think that did much, but he's definitely improved and I woke up to him playing to his cat toys which he hadn't touched previously.
Thank you all again for your help, it's really, really appreciated. :)