Took the front wheel off, as the tube not holding air at all. Tyre off, tube in bowl of water to locate puncture. Found one slit, a cut made by a sharp blade by the looks of it, less than a centimetre long. That's it: when I pinch that point, the tube holds air. So I check the smooth inside of the tyre for any corresponding cut: for the life of me I cannot find anything. Anyway I patched the tube on the front wheel, popped it in the tyre, tyre on rim, and inflated. Holding air fine, but as I inspect the tyre sidewall I see a small cut just next to the reflective strip above the rim, about 1cm, barely noticeable. So the thief must have stabbed the tyre with a stanley knife or similar. The cut is very small, but will need a tyre boot and some rubber glue or it might get bigger and then I could suffer a blowout.
The rear tyre has the same issue, except the cut there (which underlines neatly the Schwalbe logo) is over 10cm long, and shallow. The inner tube has a faint scratch and one tiny hole, which I've now patched. Hopefully the tyre sidewall is patchable/bootable, but what a hassle. In the meantime the bike will live up here on the top floor...
I went to check on the shed, no sign of anyone forcing anything, all seems to be there. Bizarrely, a rusty bike has appeared which wasn't there a couple of days ago. It's an old steel framed Giant hybrid, looks like it's been gently decaying in someone's garden for a few years: orange chain and rear mech; left twistgrip shifter busted; foam saddle has been cut and torn up, opened like a clamshell, leaving foam exposed - that looks recent. Nobody is going to be riding it anytime soon.
I can only imagine the thief/ves lifted it from a nearby colony flat garden: the bars, frame and stem still look nice, especially in the dark perhaps. Once he/they realised the bike was no good, stashed it by my shed and went looking for another one?
Complete bar stewards.