I found a very promising new ESP8266 module, from Olimex (a Bulgarian company).
It’s a breadboard-friendly board with an ESP8266 and 512k of flash memory on it, and it’s dead cheap. There’s even a carrier board for it, with a relay and a reset button, also dead cheap. I bought a couple, because it exposes all the pins from the microcontroller, so I can (a) use more than one I/O, and (b) hook up the reset pin so that I can put the device into (and, more importantly, wake it up from) deep sleep mode to extend battery life. There are videos on line of how simple it is to program these devices using the new arduino IDE.
The (insert strong adjective here) problem is that I can’t (insert strong adjective here)-well get it to work. I can connect it up to my PC fine. I can even put it into flash mode perfectly well. In neither case will it respond coherently to anything sent to it from the PC. In ‘normal’ mode, it just repeatedly sends the word ‘Error’ over the serial link, and does not respond to any AT commands.
In reflashing mode, it simply fails to respond to the reprogramming commands. I’ve tried two of these modules, and both behave the same. I’ve contacted Olimex both by email and on their forum, and had no response. It’s a shame, but I think these modules are destined for the rubbish bin. At least they weren’t expensive.
Update: Olimex have got back to me, and have made some helpful suggestions. They don’t know what the problem is, though, and it’s not one they have seen before. It may well be something to do with my serial adapter. I have another on order, so I guess I’ll find out in due course.