Blimey - what a faff!
TOP TIP: Latex tubes are incredibly stretchy, so if you get the tiniest of tiny holes in the tube, the hole can stretch when the tube is pumped up. When the tube is not under pressure, the hole can close back up again. You don't really want to put a lot of pressure in the tube when it is not being held back by a tyre, for fear of over-stretching it. Therefore, such a closed-up tiny hole can be very hard to find. I blew a little air into my punctured tube by mouth and held the whole tube underwater. I waited for 5 minutes and not a single bubble emerged!
It finally dawned on me what was happening so I went round the tube, taking a 3 inch section at a time and stretching that underwater. Eventually a stream of bubbles emerged. Stop stretching, the bubbles stopped. It was impossible to see the hole when the tube was not being stretched so I marked it with a biro before getting my puncture kit out.
I patched the hole with a standard patch. Yes, that will introduce a stiffer section on the otherwise super-flexible tube, but I don't think it will be a problem. We'll see ...
Anyway, I am having a mug of tea now before going out on my ride. If the damn tyre is flat again by the time that I am ready to leave, I will use my other bike instead!